Tommy, Author at Every Step Calculus

Difference Quotient, 7*√(x+13)

April 10, 2017 by Tommy Leave a Comment

Raw Transcript

Hello again, Tom from everystepcalculus.com. Difference quotient, regarding the square roots. And let’s do it. Index 8 you come to my menu here. I’m going to scroll down to what’s asking your test problem. Do the difference quotient to find the definition of derivative. So we scroll down here to difference quotient. Press ENTER and we under the program. Always write the formula on your paper first okay. Sometimes Delta X might be used in you from your professor for character H. So do that. Any time you see an H you’re going to put delta X okay. And then you’re going to have look at my program and change the character as you go through it. Enter the function here you have to press alpha first and enter my programs. And so the function we’re going to enter is 7 times second which is the time sign, which is the square root sign X + 13. X + 13 closed off at parenthesis. Press ENTER, here’s a few minute I will show you that so you can change in case you made a mistake it’s what we entered so that’s cool. It’s busy loading the program. And we’re going to rendering X + H for every one of these X’s in the function all over H. we get rid of the radicals by squaring them. Here’s the denominator with H. we’re going to multiply the same thing up here at the top which you can do equals 1. So you can multiply whatever and then whatever you think up on the bottom of the denominator and put it in the top. Right now we’re going to add the radicals and put in the top of the cube. Which gets rid of these okay. When you multiply radical times of radical. It becomes a not radical okay. You want to find out if we’ve gotten rid of the radicals here. No problem, you still have the radicals in the bottom of course. Expand the numerator, turns out to be this. Combined the numerator turns up by 7H. We divide the H out becomes 7 and then we have this remaining in the denominator okay. Now there’s an H here. So as H approaches 0 which is the definition of, or the rule when you’re dealing with limits. As H approaches in this case. It is approaching 0 so what an equals 0. The H comes out. And we have X + 13 plus square root of X + 13. So we get two times the square root X + 13 which is the answer is something denominator okay. So this is all basic algebra I’m in this very difficult who knows elder were this good. But I mean you can study it for weeks and know it. But I mean who wants to study it. Who needs to study it? It’s complete waste of time. So use my programs and pass calculus okay. so have a good one. everystepcalculus.com

Difference Quotient, √(x)

April 10, 2017 by Tommy Leave a Comment

Transcripts

Hello Tom, from everystepcalculus.com from everstepphysics.com. The difference quotient is what we’re going to do here. And I need to do one more because the square roots are kind of difficult because you have to get rid of the radical signs. And get of radical. You multiply times a radical and our radical squared is turns out to be whatever is inside the radical okay. So I’m going to show you kind of a very simple one here. So maybe you can learn this better or to understand it better. We’re going to scroll down here to difference quotient. Here’s the form you write that on your paper all the time we were to do that. Enter the function. And to press alpha first, alpha second. Time sign is a square root sign of X. And we’re going to this close up the prices. So in the front are going to add X + H, to every X in the function. I say it’s okay, it gives a chance to change it in case you may never stay put. And we’re loading the program here. Again the formula. So we’re going to put X + H here in the radical and we’re going to subtract the function. Visual function which is the funding divided by H. To get rid of radicals you need to multiply it. Somehow the radicals, times itself. Okay spire radical you get what’s inside the parentheses and the radical. So we’re going to here’s, the radicals here we’re going to have to put that in the denominator. Because you can’t just do it in the numerator you have to do the denominator also which actually equals 1. It’s multiplying x 1. So we look at what radicals we need to get rid of. We need to multiply that times that. And there is we’re doing that we’re putting in the denominator also okay. When you do that you get what’s inside the radical which is X + H – X okay. And we have H down here and we still have the radicals down here. We have to have that. In algebra expand it, you get this up in the numerator. We get H in the numerator and divide out the H, you get a 1. Still have an H here. As H approaches 0 when you’re taking the limit of a function. In this case that equals 0 so X + 0 is X. So you get two square root X on the bottom. Sorry this is not over here further but I have to make room in cases are extremely hard function and they take up the whole line down here okay. So you get the idea and so the answer is two times the root of X okay. This is the derivative the retribution function. Pretty neat everystepcalculus.com. Don’t waste time. Go to my programs buy them. There cheap for what you get here. I’ve studied years in this crap to help you pass calculus and of course you can buy my programs and pass calculus. So have a good one okay. everystepcalculus.com

Green’s Theorem, unit circle, 9y,3x

March 30, 2017 by Tommy Leave a Comment

0:00

Hello. Tom from everystepcalculus.com and everystepphysics.com. Another Green’s theorem regarding a unit circle and its dividend. Index 8 get to my menu scroll down to Green’s theorem year what is the only reason that we’re studying this stuff is crap is to pass our calculus test passed her test that’s the only reason we have no interest in it whatsoever unit or going to work at NASA we have no interest in it keep that in mind raising our professors charity she disliked there are some basis for some goodness 40 are evergreen serum here problem from Yahoo gets have to press alpha beforehand or anything in these entry lines here is now four times why where the axe function and three times C looks pretty good reason to I say it’s ok they gave me MRP using MNE and here and it goes as the partials hebrew 3-6 unit circle convert to pull their situations circles Mexico said it takes our way it was caught sight of theater times are and we’re gonna do the first or detain Dr agreed defeated come up with minus six times over 250 compute that come up with minus 12 hi I mean agreed that Dr in a girl putting minor stroke pioneer over 10 subtract them and we come up with minus 12 high school career. Pretty neat, huh? everystepcalculus.com and everystephysics.com. Don’t do this step without my programs. Have a good one.

Arc Length of a curve x=y^3/6+1/(2y)

March 12, 2017 by Tommy Leave a Comment

Transcripts

Hello everyone, Tom from everystepcalculus.com and everystepphysics.com. We’re talking about arc length today. Got this on a new test that somebody sent me so I’m going to do a video of it right now. Pretty complicated nonsense in calculus but still there for calculus two, people. So let’s do it, index 8, type in into the home screen there to get to my main menu. Your going to choose number 5, arc length and because the problem gives it an x, or a g a y. I’m going to choose number 2. And we’re going to, I show you the formula here, here’s the formula for the arc length and the x function given is, you have to press alpha before

you enter anything into my entry lines here. Alpha y cubed divided by 6 plus one divided by 2 times y. Looks good. I always show you which of entered, you can change it if you want. I say it’s good. I choose number 1, okay. I always show you the derivative first; take the derivative of that. I give you the choice of which system they give you too. If they give you y, then we’re cool in this system here. We just enter what they give you. If they entered x then you have to compute the y values that were given the X values. So we’re gonna do alpha 2 or, lower one is alpha 2, upper limit is alpha 3, or range, upper range. And I show you that also in case you made a mistake. I say it’s ok. We do our computations. This shows you the exact problem which is what you’re dealing with and what you write down in your paper, here. And we’re going to square that as part of the functions, here. You notice that calculus is so pathetic that they do one derivative and the rest of it is you have to do square roots, you have to do squares, you have to do integrals. Well, I do that all for you. Here’s squared. Now we’re going to add one to what we’ve squared which equals this, here. We’re going to take the square root of that whole mess right here. And we’re going to take the integral of that which is this right here. And over this range 3 and 2. Y equals 2, substitute that in for the original equation here and you get thirteen twelves, add 3 substitute that in, you get 13 over 3, you take the upper minus the lower and you come up with thirteen over 4 or 3.25 units. But pretty neat, huh? everystepcalculus.com. Go to my site and hope that I make other videos for you. Have a good one.

Linear Approximation, 1 variable, f(x) = √(x), x=49. 4

March 2, 2017 by Tommy Leave a Comment

Transcripts

Hi, I’m Tom from everystepcalculus.com and everystepphysics.com. This is a linear approximation problem in calculus one generally because one variable and we’re going to read it here because it’s off of a test using your approximation to approximate square root of 49.4. We’re going to let f of X equals the square root of x and then that can be written as the point-slope form of y equals MX plus B so we’re going to compute m and B. Let’s do it, Index 8 to get to my menu. We’re going to scroll down here to linear approximation, in the L section. And we’re going to use one variable because there’s only x given. So linear approximation, one variable, I’m going to use the point-slope form equation for a tangent line to occur y equals MX plus B. We’re going to enter function, you have to press alpha before you enter anything into these entry lines here. So it’s alpa and second X will give us the square root sign put in the X close off the parentheses. Press Enter. I always show you what you’ve entered you can change it if you want. We’re going to enter the point but you want to evaluate this at. We’re going to press alpha again and I’m going to pull 49.4. Check that make sure it’s right again. I say it’s okay. First thing we do is we enter the function and get it do the derivative of that which is the slope and it equals m. Here’s the derivative of that. And we find that the closest square root number for that given number 49 and we add that into the derivative and so the slope is equal to one over 14. Now we take that number 49 again and add it into the original function. We came up with y equals seven. So the point is 49 for x and 7 y, okay. Y equals seven, then we’re going to find B so we do the calculations here in algebra. And b turns out to be 7 halves . We found that already, ok. If you want to go further and they’re asked for this point slope form this is equal to y equals MX plus B slope times X to speak now we’re going to enter the original point where after in the same formula and so then y is equal to 7.029, okay? And the XY is 49.4, 7.029. Pretty neat,huh? everystepcalculus.com. Go to my site, buy my programs, and pass calculus. Have a good one.

How to solve: ∫(√(x))dx / √(1-x)

February 27, 2017 by Tommy Leave a Comment

Let √(x) = sin(u)

Differentiate both sides

= 1/(2*√(x))dx = cos(u)du

So:

dx = cos(u)du / 1/(2*√(x))

= cos(u)du / 1/[2*sin(u)]

Invert and multiply

= cos(u)du*2*sin(u)

So:

∫√(x)dx / √(1-x)

Substitute

= ∫sin(u ) * cos(u) * 2*sin(u) / √(1-sin(u)^2) du

= ∫ 2*sin(u)^2 * cos(u) / √(1-sin(u)^2) du

Identity

= ∫ 2*sin(u)^2 * cos(u) / √(cos(u)^2) du

= ∫2*sin(u)^2 * cos(u) / cos(u)du

cos(u) cancels

= ∫2 * sin(u)^2 du

Identity

= ∫2*[1 – cos(2u)]/2du

= ∫ [1 – cos(2u)]du

= ∫(1)du – ∫cos(2u)du

= u – (1/2) * sin(2u) + C

Identity

u – (1/2)(2) * sin(u) * cos(u) + C

u – sin(u) * cos(u) + C

Back substitute

Answer:

= sin-¹(√(x)) – √(x) * √(1-x)”

Green’s Theorem, Triangle, 3x^2+y,3xy^2

November 1, 2016 by Tommy Leave a Comment

Transcript

Hello. Tom from everystepcalculus.com and everystepphysics. com. Another example of Green’s theorem and show you how that pathetic. Index 8 lyrics to get to my menu. Scroll down to Green’s theorem. Generally in a test, they give you, your’re supposed to use Green’s Theorem or something like that. So we choose Green’s Theorem. And we enter our x and y or i and j functions. This one is You have to press alpha before you enter anything in my entry lines here on the calculator ok? Alpha plus three times x squared plus y. three times for the j or y value. Three times x press alpha. Alpha three times x times y squared. Imagine the knucklehead professor that’s still refer to which taking up these functions here that would work. That’s what they are asking for you to do. Just find the area of a triangle. Which is of base times height. I give you a chance to change it. The m or the p function is 3 x squared plus y and the q or the n function is three x y squared. It uses different letters for which professor you’re talking to or which book you use. And the partial of m, i use m here. The partial of m with the partial of y is one and the partial of n with the partial of x is 3y squared. And we subtract those going to the formula. That’s 3 times y squared minus 1. And we’re going to choose, I’m going to go up and press the up cursor to go to the bottom of the menu to get to triangle. This is a Yahoo problem. Right triangle, okay? What do they give you? They either give you 3 points or the give you this y equals, y equals, x equals. This case, it’s the first one there. Choose that. Then I’m going to go alpha zero, it chooses the boundary if you’ve ever worked with Green’s Theorem, that’s the most difficult thing is to figure out what the boundaries are. And that’s 2nd alpha, alpha x 3rd one is the x value is alpha 1. I say it’s ok. And we do the green set up. This is what we found here. For the partials these regions d y dx.

So we integrate dy.And then we over the range that was given which is a x is 0. Comes out to be x cubed minus x. And then we integrate dx. x cubed minus x with respect to x over the range of 1 0. So the answer is minus one quarter squared units. Pretty neat huh? everystepcalculus and everystepphysics.com. Don’t try to pass Calculus without my programs. Believe me, it’s much easier. Have a good one.

Published on Mar 6, 2016

Green’s Theorem, Triangle, x^2y^2+4xy^3

October 25, 2016 by Tommy Leave a Comment

Green’s Theorem, Triangle, x^2y^2+4xy^3

Transcripts

Hello everyone, Tom from everystepcalculus.com and everystepphysics.com. You can buy my programs to pass your physics and calculus classes step by step on all the problems which you need to show your work. Index 8 to get to my menu. We’re gonna do the Green’s Theorem, today, in this one. And they give us a triangle with vertices to figure out the double integral. So we’re going to choose index 8 to get to my menu and we’re going to scroll down here to Green’s Theorem it’s alphabetical. There’s Green’s theorem there. They give us the x or the i function from the line integral. You have to press Alpha before you enter anything in these entry here. Alpha x squared times y squared. And then we’re going to choose for the y the J function. Alpha 4 times x times y cubed. I always show you what you’ve entered. Here is the line integral, it really should really be called the curved integral. There are no integrals on lines. Straight things, everything needs in exponent to work. That’s the reason they use cosine and sine so much because it’s a sine wave which is a perfectly smooth curve and the use balls and spheres and etc, to do all their calculations, calculations as I see it. Calculus solves nothing in real life does nothing for anybody. Just a Soduko of math. Something that people do to waste time just like crossword puzzles in English. So anyways there’s a line integral of it and I’m going to say it’s ok to go with. P and q system or m and n system. I use the the n and m, depending on which professor you’re dealing with or the book. Compute the partials, partial of m with a partial of y is this. Partial of n with a partial of x divided by the partial of x is this . And we’re going to subtract the m from the n partials. And this right here. Ok and so now, we’re going the triangle, which they give us. We are going to choose a number to the points. They don’t give us y y x, they give us 3 points. First point is 0 0 , second point is 1 and 3, we’re going to choose number 3, scroll to it. We’re gonna add it. Alpha 1 alpha 3. And the next point is 0, 3 so we’re going to use 0 and then the question mark here, number 1

we’re going to enter number 3, alpha 3. And again, we look and see if we have entered correctly, and we have. Enter umber 1 or scroll to it. We’re going to set up the Green’s Theorem. Double integral 01 in three x Notice this, if you do the vertices and put it on a piece of paper notice that the line here is an angle such as this where certain parameters and this is the y function remember the y equals mx+b that you learned in Algebra? Well the mx is the slope and of course 3 over 1 is the slope of this line. So if you graphed it, you’d put 3x into the Y function on your graphing calculator and that would be the angle just like this. And then of course we have 3 over 0 and then 3 down the origin of the graph. So that’s the triangle we’re working with. And we’re going to integrate this right here with respect to Y and over this range here. And that equals this over the range. We take the 3x and put it in for all the y’s and we come up with 72 x to the 4 and then 0 of course is a 0. And upper minus lower is 72 x to the fourth. Now we’re going to integrate that with respect to x over this range here which equals 72x to the 5. Remember we add 1 to the exponent and divide by 5. That exponent in the problem. And over this range here. Remember Newton and Leibniz were working on exponents in the sixteen hundreds, that’s how they came up with calculus and of course logarithms, also. Logarithms is an exponent. And so we’re gonna do that range at X equals one. we substitute that for the x, come up with this, and the answer is 72 over 5 square units. 14.4 square units. Pretty neat, huh? everystepcalculus.com. go to my site buy my programs. It’s the best deal around. Much, much more economical and worth worth it then they even the calculus book. So enjoy my program and pass calculus or physics. Have a good one!

Equation of a plane

October 3, 2016 by Tommy Leave a Comment

Transcript

Hello again, everyone. This is Tom from everystepcalculus.com, everystepphysics.com. A problem with the equation of a plane that I found on Yahoo questions from a student. And I’m going to answer it in my programs here. Index 8 to my menu scroll down here to equation of a plane now and your calculator you can go second and which is quicker with your fingers and go screen by screen down to in the menu. There’s equation of a tangent plane is not what we’re looking for a look at our equation of a plane right there. There it is. And we’re given a point and a line in the problem. You have to press alpha before you enter anything into these entry lines, here. The point is 1 alpha 6 and alpha minus 4. These again all contrived problems, they never happen in real life ever. It’s just crunching numbers for no reason which is perfect for calculus. Calculus is like studying crossword puzzles to learn English. It’s a waste of time, in my opinion. But we have to pass your test we have to get through this course which you’re required to take so that’s the reason I program it for myself and I’m program for you. There’s the poin.t I say it’s ok I give you a chance to change in cases not. We’re gonna add a parametric line equation which is alpha 1+2 times t.

and the y value is alpha 2-3 times t. and the z value is alpha 3 – t. Again I show you what you’ve entered you can change. it looks pretty good to me. It’s a vector now. That’s what these little indications here are. It’s called a vector. I say it’s ok. So we do the calculations. We take T equal to zero, we come up with 1, 2, 3, here. At t equals 1 you put that in the problem. substitute one in for t’s. you’ll put parentheses in here, I have to put quotation marks because the calculation can’t go to let me do anything different and so then therefore we have 3-1 2. We have our 3 points for a plane ab&c. Here they are. And now we’re going to go find a vector from point c to b which is called vector d. I call it vector d, I call it vector d is equal to 1, 2, 3 minus the 3 minus 1 2. We do those calculations and we come up with this. Vector c to a, vector e is this. 1 6 minus 4, 3 minus 1, 2. We’re going to find the normal perpendicular well normal is perpendicular to the two vectors. Cross product, they call it normal but I mean I like to do it practical. And we’re gonna cross product d times e the two we just found which is these times this ok. Now, you try to do this from memory. Go ahead, try it; not me. It’s a waste of time. So anyway, here’s the the actual calculations. Matrix calculation multiplication and we’re doing these calculations. Make sure you write these on

your paper, now. and equals minus 25 14 8. That’s the normal vector to the two vectors we found. And so we do computations of the equation of a plane, etc Make sure you write all this in your paper, exactly like to see. And the answer is minus 25 X plus minus 14 y plus minus eight z plus 77 equals 0. pretty neat, huh? everystepcalculus.com. Go to my site, buy my programs, pass calculus. You’ll burn your calculus book but you’ll never throw away the calculator with my programs ever because you never know when your life who your partner is or your grandkids or somebody’s gonna do calculus eventually and you have all this in your calculator from then on. Have a good one.

Eliminate the Parameter, (x,y), t^2+1, t^2-1, 0

September 29, 2016 by Tommy Leave a Comment

Hello, Tom from everystepcalculus.com and everystepphysics.com. Eliminating the parameter. This is an rt equations involving t and so let’s do it index 8 get to my menu. We’re already at eliminating the parameters we scroll down to that if you scroll down with the cursor here. rt equation. This came from a Yahoo problem, a kid couldn’t do it. And of course, the people that answered the question didn’t do it very clear and of course the only thing we’re interested in is passing a test and passing Calculus and getting out of there. We have no interest in calculus beyond that. Calculus is the Sodoku math, should be taught only to math majors. It’s like it’s like being required to do crossword puzzles in if you’re an English major or trying to learn the English language to work day after day and crossword puzzles. You’ll end up with nothing. But anyways we’re going to enter the function. The function is, you have to press alpha before you enter anything in these entry lines. Alpha T squared plus one and in this for the y t, function of t. Alpha t squared minus one. Notice that these are all contrived functions. For z, we’re going to have a alpha 0. Put 0 if they don’t give you z. Nothing happens like this in real life. Calculus solves nothing I say but it does solve completely nonsense nobody ever uses it nobody ever did use it. I say it’s okay. I always give you a chance to change functions if you made a mistake but you it’s a good and we’re going to choose number five. We can do all these things to, acceleration, angle, length of an arc

etc. Right now we’re going to choose number five. Press the number or you can scroll down there press a number and try to do this without a program be my guest. Solve for t It seems simple. Y equals t squared minus one. Answer is square root of y plus 1. We substitute for t into x and z equations. There was no z equation, it was zero. And so x equals y plus 2. Notice we we put in here, you should put parentheses around this for your professor but then x is equal y plus 2. and then this equation, you want to put y equals x minus 2. and z of course is 0. You can go back for more calculations or you can go back to the main menu. Pretty neat, huh? everystepcalclus.com Go to that come to my site, buy my programs, pass calculus, keep your head on straight. Don’t let these doing that these professors scam you too much however they do all the time so have a good one.

Eliminate the parameter, t+1, 0, t^2 1

September 29, 2016 by Tommy Leave a Comment

Transcript

Hello everyone. Tom from everystepcalculus.com and everystepphysics.com. Again we’re going to eliminate the parameter. More nonsense in calculus stuff that never happens. Calculus is Sodoku of math. Let’s do it. But we have to pass calculus, we have to get these tests passed etcetera etcetera so that’s the reason I just say my programs. Index 8 to get to my menu. I’m already at eliminate the parameter, you can scroll down to it when you get your menu. Also you can use second and the cursor here to go you know page by page down to the menu and we’re going to enter our r t functions. You have to press alpha before you enter anything in these entry lines here so the first one is alpha t plus 1. And of course alpha for y is zero and alpha for z is T squared minus one. All contrived variables, of course. Here they are you can check and see if it’s correct. If it’s not, you can change them. I say it’s ok. and we’re going to choose eliminating the perimeter, number five. Again, I show you what you’ve entered here. We’re not changing we’ve already checked in already. And we’re going to solve for t in the x equation, okay. So we take x and we solve for t and t equals x minus 1. pretty simple try solving harder questions even like this one. So we put this back into x X and we get x equals x. ok no big deal there. Z is t squared minus one. So you gonna put X minus one squared minus one. Now you doing the calculations yourself you you square this and subtract 1 to get this. Let me see you do that. I can’t do it wouldn’t do it without my program why would you do I would you waste your time on this nonsense. And the answer is x equals x, y equals 0, z equals x squared minus 2x. We’ve eliminated the parameter. Okay, great. everystepcalclus.com. Go to my site buy my programs, pass your calculus test. Tell your friends about this program. Have a good one.

Definite Integral, x^(1/3)+2x 1

September 27, 2016 by Tommy Leave a Comment

x^(1/3)+2x 1

Transcripts

Hello, Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a definite integral here. It was on Yahoo so I thought I might do it. Everybody got it wrong. Didn’t even really do the integral of it right so I’m going I show you how it’s done here. Index 8 to get to my menu. Then we’re going to school down here to definite integral. And the x is given. xy is given so it’s really double integral. Still is different though. It comes up with a certain area under the curve. So we’re going to enter the function. Alpha X to the 1 dived by 3 1/3 third plus 2 times x minus one.

I always show you what you’ve entered, you can change it if you want. I say its ok. We’re gonna enter the range. Alpha 1 to alpha 8. You have to press alpha before you enter anything in my entry lines my programs and we’re gonna say that’s ok. We’re going to do the integral which is this right here and then we do the calculations it x equals 8, 8 is substitute in all these in the integral equals 68. 1 is substituted for all the X’s. three-quarters, common denominator is 269 over 4 square units or 67.3 square units. Pretty neat, huh? everystepcalculus.com, go to my site, buy programs if you want to pass calculus.

Equation of a tangent line, x^3+6xy+y^2= 8

September 16, 2016 by Tommy Leave a Comment

x^3+6xy+y^2= 8

Raw Transcript
Hello again everybody. Tom from everystepcalculus.com and everystepphysics.com.
Calculus problem regarding a tangent line with a curve. Dealing with two variables. I show you how that works on my programs. Index 8 to get to my menu. I’m already at equation of a tangent line here to save time. And you’ll scroll down to it and then you’ll enter the function Alpha, you have to press alpha before you enter anything into these entry lines. Alpha x cubed plus 6 times x times y plus y squared minus 8 equals zero. You always have to transpose everything on the other side of the equation here and bring it over the left side and make zero on the right or a number on the right either one would work. Now because you’ve entered y in here this is going to be an implicit differentiation problem. So here’s the formula here that you just entered. In the implicit system. And it looks pretty good. I say it’s ok. Differentiate both sides of the equation with respect to x. So here we go both sides. We’re going to do each one individually. This one here because xy, we need the product rule. So you can write the product rule down and do it like this or you can just keep clicking and you’ll finally get to the product rule answer to which is this right here and 6x dy dx and we keep going. y squared is equal to this because it’s a y dy dx also. And you combine the functions, dy dx here and then no dy dx just regular X Y and the implicit answer is this right here minus 3x squared minus 6x, etc. Division sign here, you know. Now we’re going to evaluate it at a point and the point is alpha 1 and alpha 1. So xy is 11. I say it’s okay. We enter those variables into the numerator and the denominator, come up with a slope of minus 98. Slope of the line and then we figure that y equals mx plus b which is here is the slope, m, and then you add the 1 for the x and 1 for the y and then figure out what b is here. Subtract this from 1, 1 of course 8 eighths and you subtract you get 17 eighths. Subtracting a minus so you get 17 eighths. Here’s the answer y equals mx plus b. Pretty neat, huh? everystepcalclus.com you can go, and I also give you that angle of the line is pointing, notice that it’s pointing in this direction not up but down to the right and if you want to do it and other points, it’ll take you back there. Pretty neat, huh? everystepcalclus.com Go to my site, buy my programs if you want to pass calculus and subscribe if you want to see more videos that I might make you. Have a good one!

U Substitution, x*e^(3x^2)

September 8, 2016 by Tommy Leave a Comment

Transcript

Hello. Tom from everystepcalculus.com and everystepphysics.com. A step-by-step process for solving an e to the x problem. Transcendental problem. Normally in my programs, if you see a cosine or sine sign and you’re integrating those and log, and e to the x, you are thinking about integration by parts, ok. But I checked for you so you go to integration by parts you and you put the those things in there and and I find out if it’s u substitution or integration by parts and then I’ll direct you in those direction or solve it that way. So, let’s do it. Index 8 to get to my menu. Scroll down to integration by parts because they’re asking this on the test program or homework problem. And integrate by parts here and of course, these are the choices here. You’re going to choose number two, e to the x and we’re gonna add our

function. You have to press alpha before you enter anything in this entry lines here. Alpha x times e to the 3 times x squared. Keep in mind the integral of e to the 3 x squared or e to the 3 x cubed, etc. This can be solved because of one of the tricks in calculus. And it can be solved because because the inside the parentheses, the derivative of this matches the outside and I’ll show you how to do that. You need to know their derivatives right away in calculus you or you’ll never get through calculus. For instance, you look at this and say the parentheses, you’re going to come up with 6x right away, not even a question about it. And 6x is close and x on the outside here so I’ll show you how to do that. Any time you enter a problem, I show you what you’ve entered, you can change it if you want. I say it’s ok. I ask you this because I’m checking whether the inside of the derivative matches the outside. In this case it does so we’re going to answer yes. This is a u substitution problem and it goes to another program u substitution so I asked you the question again no big deal we can do these things to get through our tests and homework, get through calculus. Say it’s yes and then we solved the problem. We rewrite u substitution to make it easier for instance, I took the x and put it over xdx. See it here. That’s what we’re going to match. And this is one of the big clean tricks that I’ve learned in my programs how I tell people like yourself to do the problem. U equals 3 x squared, DU equals 6x dx , you gotta take the 6 and move it over here to make the ex dx to match the problem that we just showed you in the previous screen. And then we go into you can change the u parameters. We did. The integral of e to the u is actually e to the u. That’s the reason they use it so much in calculus tests and such is because it looks complicated and it is complicated unless you know that trick. So here is the answer, 1 sixth, notice we we had e to the u with du divided by 6, you always the constants out of the integral. I just do one because it can be more complicated when we do it then 1, 10, 15 whatever. I do that for you here, too. And here’s the 1 sixth times e to the u and then we substitute back to get this. Pretty need, huh? everystepcalculus.com. Go to my site, buy my programs and pass calculus. Best deal you’ll ever make. Believe me you’ll never throw it out. You’ll throw your calculus book but you’ll never throw these programs within your titanium out. Have a good one. I’m all for you passing calculus.

ln(2x) Integration by Parts

August 20, 2015 by Tommy Leave a Comment

Raw Transcript

This video is gonna be on integration with regards to natural log. It is very difficult to me, maybe no to you, but to me it’s very difficult. You never use it so it’s tough to come up with a test or homework. So it’s good to have a program like this. That’s why I programmed it myself. So let’s get started, 2nd alpha to enter formula to get to the menu, this tells you that you can enter letters in the titanium calculator. So we enter index 8 () and press enter. Scroll to integration by parts or if you wanted to find out about log of x. So I ask you in log of x, what do want to do? Differentiate, integrate or solve for x. Some tests have solving for x and log of x which is another tricky thing if you’re not used to it. That will be in another video. So we want to integrate, so we select integrate. We are in integration by parts, when you come to log of x and integrating we will do log or x which is In(x), select and put in the example. You should see: Evaluate a In(x) Integral Exmp: x^2* In(x) Remember to press alpha to enter the formula: x^2*In(x) ,then press enter. It shows what you are trying to integrate which should be: ∫[x^2*In(x)]dx, then select ok The function will appear as follows: ∫[x^2*In(x)]dx dv = (x^2)dx v = ∫[x^2]dx = x^3/3 u = in(x) du = (1/x)dx Notice I chose the dv which is already the derivative and v would be the integration of that. So dv is gonna be x^2. And v is the integral of x^2 which is gonna be x^3/3. For those of you who don’t know how that happened, I can’t do everything exactly step by step because we’re doing function of derivatives. In the integral of the x^2, you add 1 to the 2 (the exponent) and divide by 3, so we have x^3/3. When you divide by 3 you have to multiply times whatever is in front of the x and that’s 1 so it will be 1/3 times 1/3 or x^3/3. The u choice is going to be In(x), so the derivative of In9x) is (1/x)dx. Here is the function and the formula for integration by parts ∫[x^2*In(x)]dx = v*u – ∫[v*(du)]dx =x^3/3 [In(x)] • ∫[(x^3/3) (1/x)]dx = x^3*In(x)/3 • ∫[(x^2/3)]dx Further you can see =x^3*In9x)/3 • (1/3) ∫[(x^2)]dx =x^3*In(x)/3 • (1/3) (x^(2+1) / (2+1) = x^3 In(x)/3 =-(1/3) (x^3/3) We put the 1/3 in front of the integral sign and then integrate the inside. When you’re going to integrate x^2 notice I show you we’re going to do 2+1 add 1 to the exponent and divide by 2+1. So that’s exponent 3 divided by 3. The you have your answer for function ∫[x^2* In(x)]dx Answer = x^3*In(x)/3 -x^3/9+c Check my videos out on my website, eveystepcalculus.com and of course other videos that help you. You can purchase these programs and get through calculus very easily.

Triple Integral Step by Step TI89

July 11, 2015 by Tommy Leave a Comment

Raw Transcript

Hello again everyone, this is Tom from everystepcalculus.com and everystepphysics.com. We’re gonna do a triple integral from Calculus 3 right now. this is an example of Patrick JMT, my favorite instructor on the Internet and youtube. So I’m gonna show you how it works on my program. I don’t know anybody can do that problem, he can do it because he’s a genius, but for us students, etcetera, how do we do it? So let’s get started. Index 8 to get to my menu. I’m gonna scroll up because I can go to the bottom of the menu then, instead of going down quicker to the T section and we’re gonna choose triple integral. And we’re gonna enter our function, you have to press alpha before you enter anything into these entry lines here in my programs, okay. Alpha X times sin of y. I always show you what you’ve entered you can change it if you want. And we’re gonna use the order of integration, which is dx, dz, dy, which is in the example. You have the other choices in case that’s given on a test also. region cue enter these. And we’re gonna enter the region, q. We’re gonna enter these limits. This is alpha 0 for the x one. Alpha square root of 4 minus Z squared. Made a mistake so I gotta go back. Choose number 2. Alpha 0. Alpha square root of 4 minus z So here’s what you write on your paper That’s better, say it’s okay. Next one for the y is alpha 0, alpha pi. That looks okay. and alpha 0 for the z. alpha 2. That’s okay. So here’s what you write on your paper, the way you write a triple integral with dx, dz, dy order of integration. Here’s the function in here. We’re gonna do the dx first, and you put this over here with these lines, when you’re doing the range over this integration here. And here’s the integral of the first here. Of the first function. And if x equals the upper range… I show quotation marks here but you put parenthesis in there because you’re substituting this amount for any X in the integral, and it equals this, minus sign etc. And then we do the lower integral. X equals zero, and there’s 0 plugged in, you put parentheses around this instead of quotation marks, okay. And here’s the answer, upper range minus the lower range equals this right here. So that becomes the new integration function and I show you that here. Dz, dy is left, okay? So now we integrate that, come up with this, minus sin z, z squared, et cetera and over this range here, 0, 2. Add z equals 2. Here’s the answer here, at z equals 0 plus these in for all the z’s in the problem. And the answer is this, the upper range minus the lower range is 8 sin y divided by 3. We’re gonna use that for the integration function with the range of 0 and pi. At y equals pi minus 8 cosine, here’s the 8/3. Y equals zero, you plug that in here, you get minus 8/3. Upper range minus the lower range, notice the minus times the minus, you can’t remember that stuff a lot of times. Turns out to be, the volume is 16/3. Okay. New problem. So go to my site, subscribe so you can see other videos I might make. Or you can go to the menu on my main site and go scroll down to what you need to learn. And see my program works, because it sure teaches you quicker than a book or anything else. Okay, so have a good one.

Simpsons Rule Showing All Steps

July 10, 2015 by Tommy Leave a Comment

Go to our master page for Simpsons Rule for more helpful info and step by step tutorial videos.

Raw Transcript

Hello, Tom from everystepcalculus.com, everystepphysics.com, problem regarding Simpsons Rule, person on Yahoo submitted and I’m gonna answer it on my programs. Index 8 to get to my menu. I’ve already scrolled at Simpson’s Rule, choose that, gonna add the function. You have to press alpha before you enter any of the functions in here. Anything in there, as far as variables, etcetera. So the function is alpha parenthesis 1 plus 3 times X to the X divided by 2. Here we show you what you’ve entered, you can change it if you want. This has turned into the proper formation, instead of 1+3x, you have 3x+1. You hit math, say it’s okay. And the range is given as alpha 0 and alpha 1. And he has the interval as 5, but you can’t use odd intervals in Simpsons Rule, you must use even intervals. And the more intervals you get the closer it comes to the exact approximation of the interval of the function, which we do in other ways, we don’t need the Simpson Rule, but this is another calculus endeavor. So I’m gonna use alpha 6. Say it’s okay, here’s the formula, which you write down on your paper exactly like that, and delta x, which is b minus a, divided by n, equals 1/6. Compute the intervals, at n=6 we’re gonna take delta x times these multiplication entities all the way up to six. Come up with these values here. Then, we substitute those into the original function, it’s a little bit off the screen here, I can’t do anything about that, but you can fill in the blanks there. You can see that each one of those intervals is substituting for x in here. I have quotations, you’re gonna use parenthesis. You’re gonna do it all the way till the last interval is done and here’s the computations. Use delta x divided by 3, which is in the formula, and then these are the computations of each one of the substitutions into the original function. And here’s the answer: 1.33545 is the answer. Pretty neat, huh? everystepcalculus.com. Have a good one!

Quadratic Formula App for TI-89

July 8, 2015 by Tommy Leave a Comment

Raw Transcript

Hello, everystepcalculus.com, everystepphysics.com, a problem to answer in Yahoo we have. You can see the problem here I’m gonna answer in my program with quadratic formula. Index 8 to go to my menu, this is calculus 1 now, and we’re gonna go up in the menu to get to the quadratic formula, which is right there. All steps, and shortened steps; this one wants all the steps so I’m gonna do it that way. We’re gonna add, you have to press alpha before you enter anything to these entry lines here so it’s gonna be alpha 1 for the x-squared a, alpha 70 for b, alpha minus 325 for c. I always show you what you’ve entered, you can change it if you want, we see it’s okay, we start work on the problem, you put everything down just like you see it. Exact answer and a second exact answer. Now, you can get an approximate answer by going to number 4, and and there’s the answer for 1, and there’s the -74.37 for the other. Pretty neat, everystepcalculus.com, go to my site subscribe, & see other videos I might make. Have a good one!

Shell Method and the Vertical Axis System

July 3, 2015 by Tommy Leave a Comment

Raw Transcript

Hello, everystepcalculus.com. A problem from a student regarding Shell Method and the vertical axis system. I’m gonna show you how my programs do that one. I’ll do the X axes in another video. Index 8 to get to my menu, scroll up because we got to the bottom on the menu, and get to the S section, which is Shell Method, easier, quicker. Here’s Shell Method, and get a choice of x axes or vertical axes, I’m gonna do the vertical axes now. Number 2, there’s a formula for it, and there’s always two functions given. If not, you have to enter the second, which is generally 0. You have to press alpha before you enter anything in these entry lines here. Alpha, 2, times X plus 3 is the function given. And the other one we’re going to put is alpha 0. I will show what you’ve entered, you can change it if you want. I see it’s okay. Are limits given? Yes, they are given. Lower limit is alpha 1, upper limit is alpha 2. I’ll also show you that in case you made a mistake. See, that’s okay, and you get the radius of x, and the height is 2x+3, p(x) and h(x) are the functions. So we substitute that into the formula, which is right here. You had it just like this on your paper. And we’re gonna multiply the two functions together, we get this right here with the limits of 2 over 1. And now we do the integration which equals this right here over those limits. And X=2, you substitute 2 for all the X’s in the function. I have to use quotations here because that’s where the calculator does it, but you’re going to use parentheses around these 2’s here, because you’re substituting 2 for every x. That equals this which equals 68 pi over 3. And X=1, you’re gonna substitute 1 for all the x’s in there, which equals 13 pi over 3. Upper minus lower is 55 pi over 3. That’s the answer! Have a good one!

Green’s Theorem, Triangle, x^2y^2+4xy^3

x^(1/3)+2x 1

x^3+6xy+y^2= 8

A man 5 feet tall walks at a rate 5 feet per second away from a light that is 16 feet above the ground. When he is 8 feet from the base of the light, find the rate at which the tip of his shadow is moving.