Hello again everybody this is Tom from every step calculus.com everystepphysics.com. Problems in calculus 1 regarding domain and range and regarding absolute value of a function, index 8 to get to my menu we press enter we are already at domain it gives you a chance to if in case they give you a chance to test picture to find the domain and range you can do that with my programs by saying no because we want to enter our own function and the function is absolute and we enter it this way abs parentheses we have to press alpha now when we put the parentheses in, alpha parentheses the problem is x-6 close off the parentheses and it will show you what your entering and you can change it if you want and we need to find the value of x which is, we set the absolute value which is greater and equal to zero because that is the requirement for a under radical sign you cannot have a negative sign and then I show you the graph of it and then I show you the domain the domain is all real’s minus infinite plus infinite range includes this bracket here where the parentheses which means this includes 6 and it includes 6 to a positive infinity. Pretty neat ah, every step calculus.com go on my site buy my programs and have a good time passing calculus which is a very difficult subject as you probably already know and useless to us in all of our life.

## Finding Derivative for Test Question-Video

## Derivative of ln[x^(2/3)]

#### Raw Transcripts

#### Hello, everyone. This is Tom from everystepcalculus.com and everystepphysics.com. In this video,how to do the derivative of the log, natural log of some function. And you can see function on your screen. Let’s do it. Index 8 to get to my menu. And we’re already at log of x derivative. Scroll down to that. Press enter. And we’re going to differentiate it. Because that’s what we’re doing. We’re finding the derivative. And we enter our function. In this case, you have to press Alpha before you enter anything into these entry lines on my programs. I’m going to press alpha and then it’s second to get to the log function. Here’s log of our problem. And it’s X to the two-thirds. Close off the parentheses. I always show you what you’ve entered, you can change it if you want. I say it’s okay. You press number one. Here’s the formula. Here’s over after the derivative of this. U prime over U is the formula, etc. Pretty simple but to remember all these different formulas and rules in Calculus is very difficult. That’s the reason I needed to program this stuff. The answer is 2 over 3x. Pretty neat, huh? everystepcalculus.com. Go to my site and subscribe so you can see more videos that I made you. Have a good one.

## Natural Log ln(x) Solved for Test-Video

## Solve the Equation: ln(x+2)=3

#### Raw Transcripts

Hello, again. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a, solve a natural log equation right no, on the Titanium. I’ll show you my program work on that. Index 8 to get to my menu. I’m already at the scroll down to log of x solved. Press enter and number three. Choose number three solving. You have to go through the menus. We’re going to enter the function. You have press Alpha before you enter anything into these entry lines, here. Alpha second log of X plus 2 equals 3. I always show you what you’ve entered, in programs, you can change in case you made a mistake. I say it’s okay. You’re going to multiply both sides by E. And when you multiply a log times E, you get X plus 2 simply. These are all simple but try to remember that during a test with the other any number of equations and rules you have to memorize to place into a calculus test. Pretty neat, huh? everystepcalculus.com. Go to my site, buy my programs if you want to pass calculus and subscribe so you can see more videos.Have a good one.

## Programs Included in Calculus 2 & 3 App

**Programs Included in Calculus 2 & 3 App**

Raw Transcript

Hello, everyone. This is Tom from everystepcalculus.com and everystepphysics.com. This video is on a menu of Calculus 2 and 3 if you purchased that. What you get. I’m going to go over each item and show you. Index 8 to get to the menu. The busy sign here means that it’s loading the programs. Sometimes it takes longer because of the size of the program but after it’s loaded once, it’s very quick. For instance like this F1 8 to clear, I’m going to press it now. Notice how quickly it comes up right away. I’m going to go up to the top here. And start name the things. Look at this part up here as I name them. A and B vectors, that comes in Calculus 3, generally. You’re doing all sorts of things with adding vectors and subtracting vectors and doing everything possible with them. So A and B vectors, Acceleration, Angle of Vector, Arc Length, that’s the f of x system and then the r t system, Area of a Parallelogram, Component of A Direction of B, Cosine of A and B, that’s the cosine of the A and B vectors. Cross Product, dealing with vectors. Curl computing it at a point, Curl conservative, whether it’s conservative or not, Curl whether it’s divergent, and then the systems of notation which is MNP and PQR for the curl. There’s a double integral, definite integral xy and there’s a definite integral xyz. One is area one is volume. Disk method, Divergence at a point, dot product, double integral, eliminate the parameter, equation of a tangent plane, an equation of a plane, Gradient, Green’s Theorem, Integration by Parts, Interval of Convergence, Line Integral f of xyz, linear approximation 2 variables, linear approximation 3 variables, linear equation, natural log of x the derivative of that, natural log of x the integral, natural log of x solving for x, and then log problems, those are to different bases. Mass and spring of a wire, money, p and q points, parametric equation, partial derivative, partial fractions, partial fraction decomposition, path of objects, polar to rectangle, conversion, position vectors, projection of a on b, projection of b on a, ratio test and series when you’re talking about Taylor and Maclaurin series, rectangular to polar, rectangular box, that’s a standard computation in calculus. Series Convergence, Shell Method, Simpson’s rule, Sine of x cubed, cosine of x squared times. Sketch the graph when you’re talking about p and q points, speed which is the same thing as volume. Sphere center midpoint, Sphere equation, sphere radius, Surface area of Revolution, Surface Integral xy, surface integral xz, surface integral yz. Tangent of log of x, the derivative of that. Natural log of x. Tangent of plane to surface. Taylor and Maclaurin series, Trig and half angled formulas, Trig derivatives and identities, trig integrals, triple integral xyz, triple integral zyx, U Substitution, Unit Tangent Vector, Unit Tangent PQ divided by the magnitude which is PQ. That’s those two lines there on each side of the PQ. Unit Vector Opposite, Vector length, vector between p and q, vector magnitude, Vector, unit, tangent, and Vectors. Which is taking 2 or 3 vectors and finding the angles of those vectors, etc. Quite a series of those. Vector Field Divergent, Velocity, Volume of a parallelpiped, the washer method, and that’s it. Have a good one.

## Is the Curl Conservative? Video

### Raw Transcript

Hello, everyone. This is Tom from everystepcalculus.com. A problem dealing with curl. And whether it’s conservative or not. So let’s do it. Index 8 to get to my menu. Scroll down to curl. They’re all alphabetical. Conservative. And we have the choice of PQR or MNP system. I’m going to use number two MNP system this time. And we’re going to add the function. Alpha before you anything into these entry lines, here. 2 times Y Alpha X squared plus 2 times Y times Z. And Alpha Y squared. I always show you’ve entered so you can change it if you want. I say it’s okay. This is the cross product system for doing to curl. Those are partial derivatives. And we compute each one. This is the I cartesian system. I, J, and K, etc. These turn out to be 00. Let’s see. They’re zeros and this one is not zero. Here’s the answer for the curl. Now go into the menu. Now we want to choose whether it’s conservative. So I’m going to do number one. And so here we have the the calculations and the curl again. Does this equal zero. Say no. Because the curl does not to zero, it is not conservative. So that’s the system. Try to do the curl and try to remember the cross product system of doing those calculations. I never could memorize that that kinda stuff. I have much more important things to memorize. Alright, have a good one.

## Curl Using M, N, P Notation-Example-Video

### Raw Transcript

Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. With regard to a curl, there are 2 notating systems. One, PQR and MNP. Why they chose those letters, I have no idea, in math. But that’s the way it is. Some professors use one and some professors use the other. Sometimes they use the Cartesian system which is I, J, and K, also. So I’m going to do an M, N, P system right now. Just throw in arbitrary functions and show you. Index 8 to get to my menu. We’re going to go down here to curls. We’ll go down to M, N, P. I like to, I’m going to just show you the definition of a curl, first. Curl is a vector with a magnitude (length) and direction. It represents the circulation, rotation, twist, or turning force per unit area of a field. Now that’s the best definition I can come up with because I asked that to a lot of times in calculus. I said, what the heck is this, what are you talking about? And even this, I hesitate to believe that it has any value other than some mathematical nonsense that they throw around in calculus to do these problems. A vector field is a three dimensional blob and many small vectors pointing in different directions together forming a pattern of definite form. Curl equals Twist divided by Area. A curl of F (x,y,z) is equal to the, here’s the M N P system and here’s the P Q R system defined within the Cartesian coordinates I J K. And if you’re to use the vector notation, you have these arrows on the side. M, N, P and you have arrows on the P, Q, R system. M, a function (x, y, z) in i direction. N a function (x, y, z) in j direction, and P a function (x,y,z) in k direction. Or used also is P, Q, R, etc. So now let’s do an example. We’re going to choose number 2, MNP. You have to press Alpha before you enter anything into these entry lines, here. Alpha 2 times Y squared times Z. Alpha 5 times X times Y times Z. Now these functions, I’m just dreaming up so. It’s probably going to go off the calculator. The answers. Because the screen is so small. It doesn’t go off the calculator screen on the TI-92 plus but it doesn’t on the Titanium. And then I know that you’re doing homework or experimenting because anytime an equation goes off the, think of it. The rest of your class is scored by partial credit and the class curve. Who else in the class could solve a deep problem in calculus. So will never be on a test because it’s just too hard. You would take too much time. Even if you could solve it, it would take too much time, too much paperwork, there would be no time for the rest of the problems on the test. And I have to program for tests only because of the space of the Titanium for memory use and just sanity. There’s ten million derivations of calculus derivatives and integrals. In each one of these, I have to do on a piece of paper, every one of them, to find the correct step by step process. Once I get done with that, I say it’s the best system for solving a problem but it might not be the system that your professor uses on the blackboard so you want to keep that in mind, too. Here’s the second one for the P. I’m going to put in, let’s put in Y cubed times z squared times X. oh, I didn’t press Alpha first. So we need to go back and change it. So alpha 2 times X squared times Z. Alpha 3 times 5 times X times Y squared. Alpha Z cubed. Now they seem to be correct. I’m going to say okay. Choose number 1. Here’s the matrix system for solving the curl and it’s really a cross product system. I don’t know who can remember this. I can’t, I couldn’t. That’s the reason I programmed it. Why try to memorize something when you can actually program it and have it for the rest of your life? So here’s the answers to what’s going on. With partials with respect to certain other partials. Oh the answer turned out to be not too bad, here. So now we can compute it at a point. Choose number 3. Enter the points, let’s just enter some. Alpha 1, alpha minus 5, alpha 9. Again, I show you what you’ve entered. And you substitute. These would be parentheses on your paper. These quotation marks have to be done in the programming, I can’t do anything different. And it’s substituting 1 for any X or minus 5 for any Y or 9 for any Z in the answer here. Here’s a Y right here, minus 5 but you put parentheses around that because you’re substituting. And the answer turns out to be 377. Pretty neat, huh? Have a good one.

## Curl Divergence Test Question Example-Video

### Raw Transcript

Hello, everyone. Tom from everystepcalculus.com and every stepphysics.com. Problem on Curl Divergence. Are they diverges or not and what is the answer of that. So let’s do it. Index 8 to get to my menu. Go down to curl. Don’t do the M,N,P system. Let’s do the P,Q,R system

right now. Depending on what your professor likes or does. Alpha to press anything in here. You have to press Alpha first. We’re going to put in 2 times Y and then Alpha X squared plus 2 times Z times Y, and then alpha Y squared. I always show you what you’ve entered,

you can change it if you want. I say it’s okay. Compute the curl first. Then we want to choose number 2. To the different formula. This is the system it’s not a crossproduct situation like it was in the curl. So each one is done partial of P with respect to partial of X. It turns out to be zero. The derivative of this is zero. Partial of Q with respect to Y turns out to be 2z. Partial of R partial with respect to Z turns out to be 0. So the answer is 2z. Now you want to compute it at a point. We can do that too, you can press one here, we can go to the and enter our point. Let’s enter alpha 1, alpha 5 and alpha 6. I show you again what you’ve entered, you can change it if you want. And these quotations marks are really parentheses for you. You’re substituting 6 for Z so you can put parentheses around the six on your test or homework.The answer is 12. Pretty neat, huh? Have a good one.

## Cross Product A & B Test Question Example-Video

Raw Transcript

Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. Cross Product with regards to A and B Vectors. It’s a Calculus 3 Vector problem. Let’s do it. Index 8 to get to my menu. We’re going to scroll to Cross Product. Add the vectors. Alpha 8. You have to add Alpha before you enter anything into my menus. Alpha 9, Alpha minus 4. That’s vector A. Vector B is Alpha minus 7, Alpha 8, Alpha minus 3. I always show you what you’ve entered. You can change it if you want. I say it’s okay. We’re going to scroll down to Cross Product. There’s Cross Product. A times B cross product and B times A cross product. Whichever one, they’re different. We’re going to do A times B. And it’s a matrix situation, that’s for sure. So you write these down. Make sure that you keep these in the rows that you have. Make sure you write exactly what you see, here. All these equations. This is I J, and K. That’s a different vector format. 5, 52j, 127k. and here’s the vector situation with the arrows here. 5, 52, 127. Pretty neat, huh? That’s a tough problem if you don’t have a programs, if you don’t know what you’re doing. Especially on a test or something. Go to my site, subscribe so you can see more videos. Have a good one.

## Cosine A & B Test Question Example-Video

### Raw Transcript

Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a problem for Cosine of A & B which is a Calculus 3 problem in Vectors. Let’s do it. Index 8 to get to my menu. There’s cosine of A and B, here. I’m going to add the vectors. Press Alpha first. Alpha 7, enter. Alpha minus 9, enter. Alpha minus 8, enter. Second vector B. Alpha minus 12, Alpha 8, Alpha minus 6. I always show you entered so you can change it if you made a mistake. I say it’s okay. And we’re going to scroll down here to the C’s. And there’s cosine of A and B. Here’s the formula. Dot product of A and B divided by the magnitude of A and the magnitude of B. So here’s the system that you write on your paper. Multiply this times this. And then we’re doing the magnitudes of A which is the square root of all these squares here and same thing with B. You want to try this without the program, go right ahead. It turns to be minus 108 over the square root of 194 times the square root of 244. Square root of 47 thousand. Cosine of minus 1 arc cosine of this here equals approximately 120 degrees, 2.09 radians. Go to my sites, subscribe so you can see more videos, if you want. Have a good one.Have a good one.

## Compute Curl at a Point Video

### Raw Transcript

### Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a video of a curl at a point. And let’s do it. Index 8 to get to my menu. Scroll down to the Curl, curl at a point. We’re going to do it with the M, N, P system. Number 2. Alpha, you have to press Alpha before you enter anything into these entry lines, in my programs. Z squared times Y. Alpha 3 times X times Y. Alpha Z cubed times X. I always show you what you’ve entered. You can change it if you want. I say it’s okay. Here’s the formula for the curl. Cross product stuff that’s what we’re doing. And the cross product equals this type of answers here. And the answer is this right here. So we can go back to compute it to a point. Press number 3. Alpha 2. Alpha minus 6. Alpha 9. Show you what that is, too so you can change it. And the variables go in here, in this line here and here’s the answer 936. Let’s do some other variables here. Alpha 2, alpha 3, alpha 4. 47 is the answer. In these quotations here, that’s where you put parentheses because you’re substituting the xyz values for answer of the curl. And you put parentheses around there but I can’t do that with the programming. Pretty neat, huh? Go to my site, subscribe to me to see other videos. Have a good one.

## Area of Parallelogram Program Test Question Example

### Raw Transcript

Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. Here’s a video on an area of a parallelogram. Okay. This has to do with Calculus 3. Probably with the A and B vectors. So, let’s do it. Index eight it to my menu. I’m already at area a parallelogram. Notice you can scroll down with the cursor, here. And we’re going to add the vectors. You have to press Alpha before you enter anything into these entry lines here. Alpha nine. That’s for X of the A vector. Alpha minus two. Alpha minus twelve. Now the B vector. And the X value would be Alpha 8. Alpha 6, Alpha minus 4. I always show you what you’ve entered. You change it if you want. I say it’s okay. Now we’re going to scroll down here to. This is all you do with those vectors. A plus B, A plus B magnitude. All this stuff that might come up on that test. If there’s a C, I’ll ask you for the C vector also. That’s three vectors. Cross product. Nobody can do a cross product by memory. I certainly couldn’t. Let’s do it again. Let’s scroll down to. There’s area of a parallelogram.Here’s some words right here. You can read all of that. So A times B here we’re doing A times B vectors. And then we’re gonna use that for Matrix Multiplication. The way you set it up. And then you do the various computations. I can’t memorize stuff. That’s the reason that programmed it. But it’s all correct. Mark each one down your paper. Noticed a minus times a minus, you’re always going to screw that up somehow. Look at all the minuses in here. The area equals 80, minus 60, 70 in a vector form. Now you do the square root of the squares of that. It comes up with 122.07 square units. pretty neat, huh? Have a good one.

## Calculus Q & A

### Question:

An email from a Calculus student:

Hi Tom,

First, I want to sincerely thank you for the support of your wonderful programs. You’ve inspired a knowledge of calculus that my prof cannot.

I’ve got a problem to find the extremas of an exponential function over a given closed interval but don’t know which program to use. Here’s the problems:

### f(x) = (3x-1)e^(-x), on the interval [0, 2]

and

### f(x) = (ln (x+1))/(x+1), on the interval [0, 2]

any advice would be greatly appreciated!

Thanks!

### Answer:

### In short you enter the function into my “graph by hand” menu program.

### Calculus to me is like teaching you how to multiply through the 9’s and then make a student take three semesters siting a million areas of the usage of multiplication.

### Calculus finds two things, the derivative finds the “slope of a line”, that’s it!!! and the integral finds the “area” under a smooth curve (x^2,x^3,x^4,x^5 etc and sin(x) and cos(x) (called a sine wave) as you graph those on an x y graph, and only finds the area, if you give that integral a range, called a “definite integral” an indefinite integral finds nothing.

### To me calculus is the Sudoku of math, the study of cross word problems. Something to do while waiting for a plane to Phoenix. In calculus they don’t say “rose” (ya know the flower) they say “hibiscus mutabilis” they constantly make easy things into extremely hard things. Linear approximation is a prime example, as well as related rates.

### That said, “extrema” “max and mins” of a function is the absolute or maximum high points or low points as you look at a graph of a function. If you graph -x^2 (minus) this is a smooth mountain, extrema is standing at the top. The opposite is true of x^2 (positive) this is a smooth valley, if you graph it, and you are under that valley, touching it with your finger at the lowest point.

### That said, it just so happens that when the slope of line is “horizontal” it has a slope of zero, and if you set that horizontal line on top of the mountain it will touch at only one point (tangent) and that point will be the highest possible point on that mountain. So calculus take the first derivative of a function (slope of a line), sets it equal to zero and then solves for the x values. It then puts those x values back into the origininal function, and when solved, finds the “y” value. That point (x,y) is the maximum or extrema of that graphed function. Those x values are called “critical numbers” because they lie on the x axis. They become “critical points” when you plug them into the original function and solve for “y”.

### Now to me in your first example, given what I’ve just taught you, They say “over an interval” and then give you the inteval [0,2] (Notice the brackets which indicate an interval where parenthesis would indicate a point (x,y) in math — There is only one critical point (no interval) where the hoizontal line would touch the graph (tangent), so I guess this “over the interval” is to throw you off, or check whether your understanding is as good as mine.

### My graph program will do all this for you, but in the first example if written properly (get used to doing this) would look like this: (3*x-1)*e^(-x). Notice the times sign in front of the “e” that tells you product rule to find the derivative. In the second example quotient rule would be used to find the derivative.

### Thanks, for the kudos, Tom

## Concavity-Video

# y = x^3-6*x^2-3*x+1

**Raw Transcript**

Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. We’re going to do a problem on Concavity. And I’m gonna show you how my program work on that. Index 8 to get to my menu. We scroll down in the c section to Concavity. There is is there, letter D. I always have you start a graph on your paper. You put the x axis and y-axis with these. Keep up with graphing by hand, these functions. And I have a function here of the internet, for example. You have to press Alpha before you enter anything in these entry lines. Press Alpha. And the problem is X cubed minus six times x squared minus three times x plus one. I always show you what you’ve entered, you can check it and see if it’s correct. If it is, we press okay. I know we want Concavity, number 4. I’m going to press the number here, number four. Here’s Concavity. And I give the examples, here’s Concavity down and heres concave up. This is a valley, this is a mountain type situation. See, you take the original function. Take the first derivative here which is this. On your paper and the second derivative which is this. Six x minus twelve. We set 6 x minus twelve to zero to find what the x is at that which gives us critical number, there. And with respect to the second derivative and x equals two. So here we draw a number line here with the with two in the middle. Now we’re going to choose some number above two and some number below two. And and plug it into the second derivative here. I do that for you. I say X equals three. So at the second derivative x equals three, the answer is 6. And you’ll notice the 6 is positive. That means that its going to be concave up. And it’ll look like this on the graph. If we do a number less than 2 which is one. And plug it into the second derivative and we get minus 6. So, this is negative. So this is gonna be down. And I show you this and the next screen. So this one is down when you when you graph this function, it’s going to be down like this is going to be up like. That’s called Concavity. And that’s how you do it . Now on your paper, you must write negative infinity to two and two to positive infinity. And then you’ll be correct in your test or homework. Pretty neat, huh?

everystepcalculus.com

Thank you

## Calculus Help Video

### Calculus Help using ti-89 video transcript

## Calculus Help

7/sqrt(t) |

State the domain of the function. (Enter your answer using interval notation.)

State the domain of its derivative. (Enter your answer using interval notation.)

Hello Brandon, any time you see a division sign or times sign when thinking of differentiation, first you think of converting somehow to get rid of the division or times sign. In this case the definition of derivative formula is always in x so you need to think maybe of changing the variables. t to x’s so: f(x) = 7/√(x), next since the numerator is only a constant this is not a quotient rule problem, however I realize that you are told to use the definition of derivative to get the answer. You still need to convert before you try that, so: f(x) = 7*x^(-1/2). To find the derivative you’d take the exponent (-1/2) and multiply it times what ever’s in front of the x in this case 7 to get -7/2, then take 1 away from the exponent -1/2 or: -1/2 – 2/2 = -3/2 this will give you -7/2*x^(-3/2), then convert to -7/2/x^(3/2). Now as far as my programs go I haven’t programmed that because I don’t think it would appear on any test. If it did everyone would flunk it probably. Let me know what you think, Tom

## Calculus Help: ln(x) differentiating program

# Calculus Help: ln(x) differentiating program

Hi Tom,

- If , find

3. If , find

## Quotient Rule Help

Tom,

Im not getting the right answers on the quotient rule. I plug in the values exactly as shown on the youtube video and for the f prime of x and the g prime of x my calculator is plugging in zero for both of those derivatives. Help would be much appreciated. Thanks-

A newbie to calculus

-Eric

On larger problems there is no way to see the rest of the problem or solution on the Titanium, however my theory was and is — that the programs are used to pass my tests and not to see if they can do harder problems. Large problems never appear on a test because no one would pass it. Smaller problems are tough enough and all I wanted was to not fail the class and get out of there never to see calculus again. I just needed to get a start on a problem with a formula or something or — get the problem exactly correct, showing work, I knew they wouldn’t solve all the test problems, but tests are based on curves and partial credit so I knew I’d score higher than the person next to me with the calculator help. Good luck, let me know if something doesn’t work correct. If you want to I’d appreciate any actual practice test or mid term test or quiz for you to send me so I can keep up to date on problems that are chosen for tests. Thanks,

Tom

ps I’m finishing up a better program the definition of a derivative or sometimes or also called the difference quotient, and I’ll send that to you in a day or so.

## Calculus Help

## Calculus Help

Hi Tom. How do I use this program to solve these two types of problems? What buttons do I push to locate the appropriate tools to use when solving these?