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.
Component of A onto B Text Question Example-Video
Raw Transcript
Hello everyone. This is Tom from everystepcalculus.com and that everystepphysics.com. This is a video of Component of A onto B. That’s a vector problem in Calculus 3. Let’s do it. Index eight to get to my menu. Scroll up here. It’s all alphabetical. Component A onto B. If you wanted B onto A, you have to switch the vectors around. So Vector A.. we have to press Alpha before we enter anything in these entry lines here. Alpha 7, Alpha 1, Alpha minus 2. For the B vector, Alpha three, Alpha minus five, Alpha 2. I’ll always show you want you’ve entered. You can change it if you want. Here’s the vectors. These arrows here show that it’s a vector problem. I says it’s okay. And we’re going to scroll down here to. Notice all the things that those two vectors can do. Dot product, cross product. Here’s component A onto B. Here’s the formula. Dot product of A times B times the magnitude of B. So the dot product of A and B is 7 times 3, 1 times minus 5, minus 2 times 2, etc. Total is 12. And of course we have the B where we’ve got the the square root of these squares. They turned out to be 9, 25, and 4. 12 divided by 38, the answer is 6 square root of 38 dived by 19 units. Pretty neat, huh? Go to my site, subscribe so that you can see more videos of me if you want. 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.
A & B Vector Solutions
Raw Transcript
Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. A and B vectors. This is Calculus 3, usually. Let’s get started. Index 8 to get to my menu. You’re going to have A anB vectors choose number two here. We’re gonna add the vectors. You have to press Alpha before you enter anything into my entry lines. Alpha 9. That’s the X value. If we have all the X and Y than just put zero in for Z. Alpha minus five alpha 7. That’s the first vector. Now we’re going to do the B vector for XYZ. Alpha 15 Alpha minus 4 Alpha 6. I always show you what you’ve entered. These arrows here are vectors; notations. I say it’s okay. Now you have all these choices. For instances, you want to subtract them, you choose number 4. Try this without this program if you want to try it. You’re going to mess up a minus sign. That’s what I always did or something. Got something wrong . number seven magnitude. The magnitude is this vector plus this vector. You have to that and then you have to take, then you have to multiply or use the under the square root sign. Square root of x squared y squared Z squared. Turns out to be twenty eight point seven four units. If you do number 8 . That’s for three vectors. I’ll ask you to enter the C vector. Scroll down here to cosine of A and B. That’s always fun to do. In other words, the angle between the vectors. That turns out to be this formula here. A times B times the magnitude. Add all this exactly on your paper. It’s just the way you do that computations yourself. Turns out to be 18.1 degrees and point 315 radians. Pretty neat, huh? everystepcalculus.com Go to site, subscribe for more videos. Thank you.
Limits at Infinity Test Question-Example 8 Video
Raw Transcript
Hello again, everyone. Tom from everystepcalculus.com and everystepphysics.com A limits at infinity problem. Index eight to get to my menu. You’re going to scroll or get to limits. Choose that. You’re going to choose limit to infinity. You’re going to enter the function by pressing alpha first. You have to do that in every one of my programs. And this is a test from calculus one. One divided by parentheses X minus to infinity. I’ll show you what you’ve entered, you can change it if you want I say it’s okay. We’re dividing it by the greatest power in the denominator. In this case is X. One is the numerator. So one over X is equal to one over X. And when you substitute infinity for X, it becomes zero. Denominator is X over X or three over X equals one or three over X. And 0 divided one, the answer is zero. These are all simple if you really know the trick. If you don’t they can be trouble.
Partial Fraction Example 7-Solved by TI-89 Video
Raw Transcript
Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. Partial Fraction test problem. Index eight to get to my menu. Choose or school to Partial Fractions. I’m already there. To save time on the video. Press Alpha to enter any formulas into these entry lines on my programs. Alpha first. This one is alpha 5 divided by, alway parentheses. You can’t use too many as far as i’m concerned. Parentheses make everything clear. And certainly needed in division or fraction problems. Plus 3 times X minus 4. I always show you what you’ve entered. You can change it if you want. I say it’s okay.We factored the denominator, you noticed there’s two factors here. That means you’re going to be two partial fractions. So, you start by writing five which is the numerator divided by x squared plus 3x minus 4 times the denominator not factored yet. And then you to the partials. A divided by X minus one, which is the first factor and B divided by x plus 4, whic is a second factor. Always set that up. There is no x squares or anything so it’s very simple, here. Now when you multiply both sides by by the denominator you can eliminate a denominator in your left side. So you’re going to get just five and then course, when you do the multiplication in the denominator here,they switch around. A times x plus 4 plus b times x minus one. Now again, we try to we try to look where we can eliminate certain fractions here for factors. So you notice that minus 4 plus four zeros, it would limit this would it would make a minus five here. So anyways, at x equals minus 4. You get 5 is equal to, whenever you do these, you see quotation marks. I can’t put parentheses in the calculator. The way it works so. You’re gonna put parentheses here.Parentheses minus 4, parentheses plus 4. We are inserting this into the function so that you can do the math on it. Parentheses minus 4 parentheses minus 5. You can see B equals minus 5. So B equals minus 1. And same thing here at X equals one. This becomes zero B and this one becomes 5.So A equals one. Partial Fractions are one over x minus or plus -1 over X plus 4. And you do the integrals. You got 1 times log of x minus 1 absolute and minus 1 times log X plus 4 absolute plus C. Integration doesn’t become completed remember integration solves the original funtion, finds the area under the curve of the original function. But when there’s no limit or no range yet, then there’s always a plus C here.Plus constants. If we’ve had a range like from X equals 7 to X equals 10 or something, then we would come up with a number. And that number would be the area under the curve the original function. That’s all integration does, ever. Pretty neat, huh? everystepcalculus.com and everystepphysics.com
Got to my site, think about buying my programs. Thank you.
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
Partial Fraction Example 6
Raw Transcript
Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a test problem on Partial Fraction Decomposition, again.Let me show you how my programs work on this. Index 8 to get to my main menu. And we scroll down the Partial Fractions which is in the menu. You can scroll up or down here with the cursor. You have to press Alpha before we enter anything in these entry lines here.Press Alpha and the problem is one divided by, I’m going to use parentheses for the denominator And numerator. This one is x squared minus nine.I always show you what you’ve entered. Now notice that x squared minus nine is a difference of squares so when you factor that it’s always X minus three times x plus three. And that’s a big deal in calculus so always always be on the lookout for these type of things. These difference of squares. Sometimes I’ll have X minus 3 up in the numerator and it will cancel and they use all kinds tricks to throw you off. If you’re hip and I’m gonna try to make you hip, you’re always are looking for the difference in squares. Okay. We’re doing Partial Fractions so I say it’s okay. I’ll always give you a change it if it’s not. And I factor it for you. Here’s x minus three times x plus three. If you can’t factor the denominator, you can’t do Partial Fractions. So keep that in mind, too. And the problems have to be relatively simple in tests because not that many people, including myself, are not very good factoring. In our heads, you know. They get more complicated than this, so. So, you start out by putting one,numerator, divided by x squared minus 9 times x squared minus nine. What you’re doing is multiplying both sides the denominator. This is factored but this is not. And of course, when you multiply the numerator by this, you’re going to eliminate. So there’s going to b one up there. And of course these switch around as we do times this portion here. A divided by x minus three plus B divided by x plus three. I switched it around now so it’s one equals A times x plus three plus b times x minus three. Now the first thing you want to do is eliminate some of these. So you’re going to put a minus three here to make this zero. I’ll do that for you. I have x equals minus three. I put, anytime you see quotation marks, you put parentheses. Parentheses minus three plus three which is zero. B times parentheses minus three parentheses minus three which is minus 6. Zero minus six so one equals a B minus 6. One equals B minus 6 to B is equal to minus one sixth. And X equals three parentheses three in here. open and close plus three And this becomes six and this becomes zero. Which a is equal to one sixth. Partial Fractions, enter one sixth divided by by X minus three plus minus one sixth divided by X plus three. Those are the Partial Fractions. And when you integrate these, one sixth logged absolute value X minus three plus minus one sixth times log absolute value X plus 3. So add all the stuff on your paper and homework, or whatever. Get the problem perfect. Pretty neat, huh? everystepcalculus.com. Go to my site and buy my programs.
Thank you
Limit at Infinity Example 1
Limit to Infinity Example 2-Solved by TI-89 Video
Lim (7x^3+9(x^2+3)
–> Infinity
Raw Transcript
Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. I’m going to do another Limit to Infinity problem. Index 88 to my menu. Choose Limits. Scroll to compute limit. Enter the function by pressing alpha. This test problem is seven times x cubed plus nine. Uh oh, I forgot the left parentheses. Press second, go there quick. Divided by x squared plus 3. Add the Infinity indication. Choose the other button, and the yellow register is underneath. See the yellow letters, that’s what that does for us to that register when you press the yellow button there. I always show you what you’ve entered, you can change it if you want. which you better you can change it if want. You’re dividing everything, every term in that problem by the highest order term in the denominator. This here equals this and then we add infinity to these, it’s going to come seven because anytime you take a number. So when you multiply times Infinity it becomes Infinity. So here’s Infinity and second one is zero.Numerator Limit is Infinity. Denominator divided by the highest order term of denominator is this. That equals. When you’re add Infinity, that equals one zero. The Denominator limit is one. The Problem limit is Infinity then. Infinity over one. Pretty neat, huh? everystepcalculus.com, visit my site and buy my programs. Thank you
Limits to Infinity on TI-89 Q4
Lim (7x^3+9)/(x^2+3)
Raw Transcript
Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. I’m going to show you how to do a Limit at Infinity, on this video. I’m doing several of them so you can get a great idea of what happens.Index 8 to get to my menu. Limits, Choose Compute Limit. Enter the function. Alpha Seven times x cubed plus nine. Oops forgot the other parentheses,
So we press second and the arrow here to get quickly over to the beginning. Add our parentheses and press second and the right arrow to get back where we were. precedent for a second and the right. Divided by parentheses x squared plus three. Need to add the Infinity. Yellow button here.I show you what you’ve entered. You can change it if you want. I say it’s okay. Again, we divide all the terms by the lowest ordered by the lowest quartered term in the denominator. And that equals this for the numerator. And when you do Infinity, the Numerator Limit is Infinity.Denominator…you take those terms and divided by x squared also. Equals one. Infinity divided by one is Infinity.That’s the answer. Problem Limit.
Pretty neat, huh? Visit my site and buy my programs. Thank you
Limits at Infinity on TI-89 Video
Raw Transcript
Hello again from everystepcalculus.com and everystepphysics.com. Another Limit to Infinity problem. Let’s do it. Index 8 to get to my menu. Choose Limits. Choose Compute Limit. Alpha before you enter anything in here. Alpha, parentheses, three times X plus two divided by x.
Add the infinity sign. Alpha yellow button here in the catalog which is the register for infinity. Show you what you’ve entered. I say it’s okay. We take all the terms and divided by the lowest order. X in the denominator, 3 0, the numerator limit is three. Denominator divided by Xis one. Answers is limit is three.
Calculus Q & A-Limits
Question:
Evaluate the limits:
lim(theta symbol–>0-) csc theta symbol
lim(theta–>pi/2) 1/2 tan theta
Calculate this limit at infinity (+/- infinity) for the following function:
f(x) = e^x+e^-x/2
Answer:
When you say f(x), calculus and programmable calculators are saying “y”. When they ask you for a limit, it is a trick question meaning find y. They then give you an x value and say as x approaches 5 (for instance) what is the limit? You then would plug 5 in for x ( which my programs do) and the answer is the limit is the value of “y”. Most of the time they trick you again do to the function they give you which is always a fraction such as (3x+7)/(x^2-4), (always a division sign). Then they ask you as x–>2 (as x approaches 2) what’s the limit. You’ll notice that when you plug in 2 for x you get a zero in the denominator which becomes an “undefined” answer.
If you then (like my program does) add some very small number to 2 such as .001 to get 2 + .001 = 2.001 or take a small number away from 2 to get 2-.001 = 1.999. Setting that equal to x then you actually get a number and that is the limit. I would actually graph the original function quickly on the calculator so I could see the picture of the function and then use the cursor to scroll back and forth at the x value they give you to do things like what happens when x approaches this from the right or left, to give me any clue of what their talking about.
Same thing with infinity. Graph the function first and then logically think about what they are asking. Also start to make things perfectly clear in your calculation examples so there is no question of what you’re asking.
For instance, you have:
f(x) = e^x+e^-x/2 which to a calculator, and me, means
f(x) = e^(x)+e^(-x)/2
and when you mean to say:
f(x) = e^(x)+e^(-x/2)
The problem says calculate the limit at infinity. I would graph the function on the calculator. You can see it’s just a parabola (valley looking, because no minus sign before it).
Here’s what they might be looking for:
f(x) = e^(x)+e^(-x/2)
Convert to:
= x*ln(e)+(-x/2)*ln(e)
factor out the ln(e)
= ln(e)[x+(-x/2)]
ln(e) = 1 So:
(1)[x+(-x/2)]
The limit as x-> ∞
= [ ∞ + (-∞/2)]
= ∞
Partial Fraction Decomposition Ex 11
Partial Fractions Example 3
Limits: Negative Infinity on TI-89 Video
Lim (7x^3+4x-17)/(4x^3-x^2)
Raw Transcript
Hello Everyone, Tom from everystepcalculus.com and everystepphysics.com. A problem regarding limits at Infinity. Index 8 to get to my menu. Scroll down to Limits. You can actually use second to go quicker on the menu, in other words, I want to go up a screen second, and up, second and up,or second and down. And here’s Limits. Click on that. And my other videos that I did previously I didn’t put Limit to Infinity here. You would access it by going to Compute Limit but when you want to put minus Infinity in there. It’s a little bit tricky do that. Well, it’s a little tricky on the Titanium to do that so I decided to put it in a actual menu. So here’s Limit to Infinity. We’re going to put the function in. Press Alpha first. Alpha left parentheses. This is a test problem. 7 times X cubed plus 4 times X minus 17, right parentheses, divided by, left parentheses, 4 times X cubed minus x squared, right parentheses. And let’s go negative infinity. Number two. And there it is there. This is the limit of this with X going to minus infinity. And I always show you if that’s correct. I always give you a change it in my programs. I say it’s okay. Then we’re going to divide all terms by the highest order term in the denominator. Which will be x cubed. Here’s the terms numerator. All divided by x cubed. Here’s the results. Now we put Infinity in for every X. Or minus Infinity, sorry. And that turns out Numerator Limit of 7. These turn out to be 0. Denominator
4 divided by the x cubed. That equals 4. And x squared divided by x cubed equals one over x. We add the minus Infinity to every x.
It turns out to be 40 Denominator Limit. The Problem Limit therefore is seven divided by four or seven fourths. Pretty neat, huh? everystepcalculus.com Go to my site and buy my programs. If you want to pass calculus and/or do your homework. And remember you’ll have these programs for life if you do that.
Limits Infinity Solved TI-89 Video
Raw Transcript
Hello Everyone. Tom from everystepcalculus.com and everystepphysics.com. Limits to Infinity. Let’s get started. Index 8 to get to my menu. Scroll to limits and choose number 2, compute the limit.And the function, you have to press alpha before you enter anything in here. Alpha left parentheses five plus two times X. This appeared on a test. Divided by,left parentheses, 3 minus X right parentheses.
Then press alpha and we press this yellow button here which goes to the letters with the yellow letters about the keys. The yellow register, I call it. And this is infinity right here. Alpha. There’s Infinity. I always show you what you’ve entered. The limit of two times x plus five over 3 minus X, as X approaches infinity. That’s the way you state it. I will show you what you’ve entered, you can
change it if you want. I say it’s okay. You divide all terms by the highest order term in the denominator. And that becomes a minus X
And you take the limited as that approaches infinity and the numerator limit is minus 2.Denominator, you have three and minus x in the denominator and that’s divided by minus x.Three minus x and you take the limit, you put Infinity in here. Anytime you take a number and divide it by Infinity, you get a very large number. It gets smaller and gets closer to zero. So that equals zero. And the other one equals one. That’s the denominator limit. You divide that numerator by the denominator, of course and you get minus two for the problem. Pretty neat, huh? everystepcalculus.com Go to my site and buy my programs.Thank you
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