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Hello, Tom from everystepcalculus.com and everystepphysics.com. Double Integral today. On this video. Um, so let’s do it. Index 8 to get to my menu. We’re going to scroll down to the D section. You can use the second and then the arrow to go, you know, quicker. Screen by screen. But there is Double Integral right there. And we’re going to enter our function and we’re going to press Alpha first before you enter anything into these entry lines, here. Alpha X times Y plus X squared times Y cubed. I always show you what you’ve entered, you can change it if you want. And now we have to decide whether we want to do it from dy, dx or dx, dy, that’s the order of integration. We’re going to go with number 2, dy, dx. And here we have if dx is on the outside then it’s on the outside here and this is on the inside therefore the ay by is, the limits are involved with the dy inside. So remember that. dx is on the outside therefore these go with the dx. dy is on the inside the limits of integration go from ay to by. So let’s enter those now. And there’s the region. Just like this in notation. So we’re going to do Alpha 1 to Alpha 3. Say it’s okay. We’re going to do Alpha 0 to Alpha 2. I say that’ okay. And there’s out integral right there. We have the function inside here, dy dx. And here’s the x on the outside and the limits of integration 0 to 2 on the inside. So with respect to Y, we integrate with respect to Y. Here’s the answer x squared times y to the fourth over 4 plus x times y squared over 2. And we’re going to do that over the 0 on the 2 limits. So at x equals 2, you add. You see quotation marks here but I can’t, I would like to put parentheses in for those because we’re substituting y equals 2 for all the y’s in this function, here. So you’re going to have to put the parentheses in every time you see quotation marks, put parentheses, okay. And then 4 squared plus 2 x and that’s what that equals and then y equals 0 and then here’s the 0’s in for Y and that equals 0. And 4 x squared plus 2x minus. The upper limit minus the lower limit is 4x squared plus 2 times x. Now we integrate that with respect to the limits 1 and 3 with respect to x. So we integrate that. Here’s the answer here. 4x cubed divided by 3 x squared over 1 in 3. The limits. And x equals 3 here, we’re substituting 3 in for all the x’s equals 45. And x equals 1. You substitute 1 for all the x’s, you get 7/3. So upper minus lower 45 minus 7/3 equals the are is 42.7 square units. Remember the an integral always gives\you the area under a curve. And so I always put square units in there. Alright, have a good one.
Archives for 2014
Definite Integral with (x,y) Video
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Hello, Tom of everystepcalculus.com and everystepphysics.com. A definite integral over X and Y. Let’s do it. Index 8 index to get to my menu. Scroll down to D section. Definite Integral X over XY. Double Integral. Enter the function. Alpha before you enter anything into the entry lines. This one on the internet. X times Y squared divided by parentheses, you always put parentheses in denominators. X squared plus one. I don’t know who dreams up these functions but somebody does. Remember, we’re not learning calculus for life long desires unless you’re a math major. We’re learning Calculus to pass a test. To get through Calculus. Never to touch it again. Keep that in mind, okay. Press enter here. And see if that’s what you entered. I say it is. And we’re do it over to DY, DX. And remember that D you integrate with respect to Y first when it’s DY here and DX second. And so DY is these limits of integration. And DX is these limits. So the limits given in this problem were X for 0. Alpha 0, Alpha 1. And for AY was Alpha minus 3. And Alpha 3. And here’s the Integral right here. And we’ve done the integral with respect to Y. Here’s the answer: X times Y cubed divided by 3 times x squared plus 1. And we’re going to do that over -3 and 3. So when Y equals 3, you enter these quotation marks are where you enter parentheses on your paper. Okay. Because that’s substituting Y for anything in these functions, these answers. Another one, -3 is when Y equals minus 3, these is the, you put parentheses around quotations marks. This is the answer. This is the answer for when you put three up there and you subtract the upper limit from the lower. and you get 18 X for x squared. Now we’re doing the integral of that answer over 0 in 1 limits. So we do on the integral of that which equals 9 times log of X squared plus 1. At x equals 1, this is the answer. 9 times log over 2. log 2 and x equals 0. 9 times log over zero x squared plus one which equals zero. Upper limit from the lower is this minus the 0. And so this is the answer also but when you work it out, it comes up to 6.24 square units. Pretty neat, huh? Go to my site and subscribe it you want to see more movies.
Curl Using PQR Notation Example-Video
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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. Curl problem using the PQR System of Notation, for variables. So let’s do it. Index 8 to get to my menu. We’re going to scroll down to Curl. You can hold that button down or you can just press it each time to go down. Here’s P Q R, Curl PQR. We’re going to choose that. Do a Curl problem. Choose PQR again. That’s what you’re doing. That’s how it’s notated. Cartesian up here and vector notation here with the arrows on the ends. We’re going to use these up here. Alpha Y times Z squared. Alpha, you have to press alpha before you enter anything into these entry lines here. Alpha X times Y. Alpha Y squared times Z. I show you what you’ve entered, you can change it if you want. I say it’s okay. This is the tough part do the cross product of partial fractions, here. That’s tough. You gotta remember that and what to do. That’s why I programmed it so you never make a mistake on it. It’s mindless stuff so why ponder it. Put it in a program and use it. Here’s the computations of that. I J K is Cartesian. I is X, J is Y, and K is Z axis. And here’s the answer here. Okay. Now we can do several things but let’s compute it at a point. Number 3. Compute the curl at a point. Let’s enter Alpha 1, Alpha 2, Alpha 3. Again, I show you what you’ve entered in case you made a mistake. It puts the x and the y and the z values into this formula. The quotation marks are there, you should use parentheses where you see quotations. Because your’e substituting 3 for x or Z, in the case Z squared plus 4 times Z times 2 which is Y plus Y. And the answer is 17. Pretty neat, huh? everystepcalculus.com. Goto my site, subscribe to see more videos. Have a good one.
Vectors-Magnitude of A times B
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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. This is an everystepcalculus.com problem. And with my programs. Question on vectors. Let’s get started. Index 8 to get to my menu. Choose A and B vectors. This is a Calculus 3 problem. This student wanted to know how to find the magnitude of A times B. He could get the cross product but he do the magnitude of it. So, let me know you how to do that. You have to enter Alpha before you enter anything into these entry lines, here. So, Alpha minus 2. Alpha one. Alpha one. For the B Vector. Alpha 2, Alpha 1. Alpha 1. So we check see if that’s the vectors that you want. I say it’s okay. A times B is the cross product so we’re going to go to here, A times B. Matrix Multiplication. Write this on your paper, exactly as you see it. There’s the Cartesian System. Notating a vector. Right here. And here’s the answer for the cross product. Zero, four, four. So, we have one vector now which is 0 for X, 4 for Y, and minus four for Z. So now we’re going to go down and we’re gonna find new AB vectors. As we need to put a new vector in for A. So the answer was Alpha zero, Alpha four. That’s for the cross product. Alpha minus four. And we can just quickly go through these because there is no vector for B of A. So now we’re going to go up here and find magnitude of, magnitude of A, number 2. Choose that. This is the way you notate it, it’s got these two lines on the side. It’s called the magnitude of A. Do these calculations. Notice the square root of x square, y squared, z squared and we come up with 5.66 units. Pretty neat, huh? everystepcalculus.com. Have a good one.
Programs Included in Calculus 2 & 3 App
Programs Included in Calculus 2 & 3 App
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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.
U Substitution Solver-Video
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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a U Substitution problem. Basically a simple one but nothing is simple in Calculus unless you know what you’re doing. It certainly helps to have a photographic memory. This problem was sent to me by a student. I’m going to do it on the video and show him how to do it and show you how to do it. Index 8 to get to my menu. U Substitution. You’d scroll down to it there. Choose that. We’re going to enter the function. Alpha, left parentheses 6 times x minus 5, close off the parentheses to the 4th power. So here’s what we have. I say it’s okay. So let’s talk a little bit about U Substitution. You should do derivatives in your head within one second. What’s the derivative of this function in here? It’s 6. There’s no x’s nothing, it’s just 6. And you have dx on the outside. Okay. So there’s no x or nothing else on the
outside except dx. So let’s, that’s what you choose for U. So U is 6x minus 5, derivative is 6dx, anytime you see a constant on here. This is the trick that always screwed me up in school. You need to take this out of this side and isolate the dx. Okay, because remember the dx is by itself on the function and now this dx needs to be by itself like here. So you divide both sides by 6 through Algebra. DU divided by 6 equals dx. It variably happens like this. Don’t think it doesn’t. Almost every problem you do on U Substitution, your’e going to take the constant from this side and put it over on this side. Okay. So no U equals 6x minus 5. Therefore, the integral of u to the 4th is the function, u to the 4th times du divided by 6. Now here’s the du we just did, du divided by 6. In integration, the constants always have to come out of the integration. So you have to take one sixth out which I do here. Here’s one sixth out of the integral. And here we have the u to 4 by itself, and the du is by itself. Okay. So now we got one sixth times, and now we do the integral,u to the 5 divided by 5. Okay. So now this constant has to come out of here, too. So we have one sixth times one fifth times u to the 5 plus C. Well one sixth times one fifth is one 30th times 6 and then we substitute back in for u, 6 times x minus 5 to the 5 power plus C. Every U substitution is not in the system and if you learn this system, you’re going to be alive but the main thing is to be able to do derivatives in your head in one second. In your sleep. The derivative of this right here is 6 and you need to look and see if you can match something on the outside, etc. For U substitution. It’s all tricky though until you do it ten thousand times. Calculus is a language and most the cases when I was going to school, it was learning Latin or learning Spanish. I didn’t know what they were talking about. So, have a good one.
Integration by Parts-Question by Student-Video
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Hello, this is Tom from everystepcalculus.com and everystepphysics.com. A student had a question about E to the X integrals. Integration by parts so let’s do it. Index 8 to get to my menu. We’re going to scroll down here to Integration by Parts. To the I’s, there it is. Waiting for it to load. Whenever you see a busy signal, it’ means it’s loading. Sometimes it will take long but after it loads once, it’s quick. And we’re going to go e to the x problem. Busy again loading another problem. We’re going to enter the function that he was wondering about. Alpha x times yellow key x for the e x and close off the parentheses. I always show you what you’ve entered. You can change it if you want. I say it’s okay. Number 1. Does x equal 1? No, we’re going to choose number 2. That means it’s an integration by part. Otherwise, it’d be a u substitution problem. We’re loading another problem here. Here’s the formula for integration by parts. DV and V is the integral of e to the x. U is x, etc. Here’s the formula. You want to put that all together and write it on your paper. And here’s the answer. X times e to the x plus a minus e to the x. Pretty neat, huh? everystepcalculus.com. Go to my site, subscribe to them so you can see other movies. Have a good one.
Is the Curl Conservative? Video
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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