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

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Hello. Tom from everystepcalculus.com and everystepphysics.com.  A step-by-step process for solving an e to the x problem.  Transcendental problem. Normally in my programs, if you see a cosine or sine sign and you’re integrating those and log, and e to the x, you are thinking about integration by parts, ok.  But I checked for you so you go to integration by parts you and you put the those things in there and and I find out if it’s u substitution or integration by parts and then I’ll direct you in those direction or solve it that way.  So, let’s do it. Index 8 to get to my menu.  Scroll down to integration by parts because they’re asking this on the test program or homework problem. And integrate by parts here and of course, these are the choices here.  You’re going to choose number two, e to the x and we’re gonna add our
function. You have to press alpha before you enter anything in this entry lines here. Alpha x times e to the 3 times x squared. Keep in mind the integral of e to the 3 x squared or e to the 3  x cubed, etc. This can be solved because of one of the tricks in calculus.   And it can be solved because because the inside the parentheses, the derivative of this matches the outside and I’ll show you how to do that. You need to know their derivatives right away in calculus you or you’ll never get through calculus. For instance, you look at this and say the parentheses, you’re going to come up with 6x right away, not even a question about it.  And 6x is close and x on the outside here so I’ll show you how to do that.  Any time you enter a problem, I show you what you’ve entered, you can change it if you want. I say it’s ok.  I ask you this because I’m checking whether the inside of the derivative matches the outside. In this case it does so we’re going to answer yes.  This is a u substitution problem and it goes to another program u substitution so I asked you the question again no big deal we can do these things to get through our tests and homework, get through calculus. Say it’s yes and then we solved the problem.  We rewrite u substitution to make it easier for instance, I took the x and put it over xdx. See it here. That’s what we’re going to match.  And this is one of the big clean tricks that I’ve learned in my programs how I tell people like yourself to do the problem. U equals 3 x squared, DU equals 6x dx , you gotta take the 6 and move it over here to make the ex dx to match the problem that we just showed you in the previous screen. And then we go into you can change the u parameters. We did. The integral of e to the u is actually e to the u. That’s the reason they use it so much in calculus tests and such is because it looks complicated and it is complicated unless you know that trick.  So here is the answer, 1 sixth, notice we we had e to the u with du divided by 6, you always the constants out of the integral. I just do one because it can be more complicated when we do it then 1, 10, 15 whatever. I do that for you here, too. And here’s the 1 sixth times e to the u and then we substitute back to  get this.  Pretty need, huh? everystepcalculus.com. Go to my site, buy my programs and pass calculus. Best deal you’ll ever make.  Believe me you’ll never throw it out. You’ll throw your calculus book but you’ll never throw these programs within your titanium out.  Have a good one. I’m all for you passing calculus.

Calculus Rate of Change | Mans Shadow Problem

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

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everystepcalculus.com. Related Rates problem concerning a shadow of a man and a light pole. Index 8 to get to my menu. We’re going to scroll down to Related Rates, here. Here’s related rates there. Then we’re going to scroll down to shadow. Lamp post, person, shadow changing. Here’s a picture of it. And the lamp post is given as Alpha 16 feet high. You have to press Alpha before you enter anything into these entry lines, here. A mans rate of change is Alpha 5 and it is increasing because he is walking away from the lamppost. And the mans height is alpha 5 feet, the distance given is alpha 8. I always show you what you’ve entered, you can change it if you want. I say it’s okay. I show you the definitions of what we’re talking about. Now we do the calculations. You write all this on your paper, of course. Exactly as you see it. And so the change of is 88 over 11 feet per second. Now you can work this out if you want to, you know with a calculator. 88 divided by 11, this is the exact answer. And the second part of the problem. What’s the length of the shadow changing? And you do this calculation here. It turns out to be 25 over 11 feet per second. And you can do the approximation if you want on your calculator. Have a good one.

 

ln(2x) Integration by Parts

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

Triple Integral Step by Step TI89

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

Simpsons Rule Showing All Steps

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

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

Quadratic Formula App for TI-89

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

Shell Method and the Vertical Axis System

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

Partial Derivatives First Order

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Hello again, everyone, this is Tom from everystepcalculus.com and everystepphysics.com. I’m gonna do partial derivatives now in this video, generally with respect to calculus 2 or 3. Let’s do it. Index 8, get to my menu… Scroll up to get to the P’s quicker. It goes to the bottom of the alphabet, so we get to what we’re looking for, it’s partial derivatives. On the menu you can go second and the titanium second and then these cursers to go page by page. You do that here to get through the menu quicker, and we’re looking at, let’s see, partial fractions, here’s partial derivatives, and I programmed first order or second order; we’re going to do first order in this problem. Z= f (x,y) We’re going to enter our function, that the function given is. You have to press alpha before you enter anything into these entry lines in my programs, okay, so alpha, and then we’re going to press T here, which gives us the arc tangent for Y divided by X I always show you what you’ve entered so you can change it if you made a mistake. So it’s okay, and here’s the partial derivatives, with respect to x, is minus Y divided by X squared plus Y squared, this is a, if you go to my trig identities you’ll see that tangent to the minus 1 is 1 over the quantity of 1 plus x squared. In this case it would be 1 over the quantity 1 plus Y divided by X squared. To get the derivative with respect to X and with respect to Y, it’s this equation here. And then there’s a point A and B that they give you. Press the one for A, is alpha, minus 2. Make sure you know it’s interchanged the minus sign for the negative sign. And then for the B, alpha 7 is given. Again I’ll show you what you’ve entered, and we see that’s okay, and so the problem asks for fx(a,b), which is this right here, replacing the y’s and the x’s for whatever is given here for A and B. And I have to use quotation marks the way the calculator allows me to with programming, but you’re going to use parentheses here anytime you see a quotation here, because you’re substituting X and Y values for the X and Y values in the function. And the answer is -7 over 53. And now if they ask you for F of Y you’d go one step further, and that would be substituting this, you get -2 over 53. Pretty neat, huh? everystepcalculus.com, go to my site and subscribe to me so you can see other videos if you’re interested. Have a good one!

Calculating Integral with Shell Method

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Hello, everystepcalculus.com. We’re gonna do a problem in Yahoo regarding Shell Method and show you how that’s done in my programs. Index 8 to get to my menu. Then I scroll… if you go up, you get to the bottom of the alphabet because S is closer to W than A. And then we’re gonna find shell method, which is there. This problem is vertical axes number 2. Shows you this formula. They ask you if p(x) is the radius and is this second value given for X, and yes it is. We’re gonna add that alpha. 4 times X squared and the next value for Y is given. Alpha 24 times x minus 8, times X squared. I always show you what you did, and that was not correct so I have to go back and change it. Alpha 4 times x squared… I don’t know why it wasn’t right. Alpha 24 times X minus 8 times X squared. That’s better. Say it’s okay. Are the limits given, no, they’re not given. So we have to compute the limits, so we choose number 2. We do that by setting the… if no amount is given for the x axis of revolution then the vertical axis is 0; x=0. Anyways, we set the two functions equal to each other and then solve for x, when x equals 0 or 2. That’s where these functions intersect the X values where the Intersect. And so the height then needs to be recalculated. Height is the original function less than p(x) which equals this here. And then we’re ready to do our here’s the limit, 0 and 2, we do the calculation. Here’s the volume for the solid, the formula, notice x is for the radius and this is for the heights. And we multiply them together, we get this here. And we do the integration, which is this this: 8x cubed minus 3x to the fourth. And then at x=2, I’ll show you, these quotation marks here are you’d put parenthesis in there because you’re substituting 2 for all the x values. That equals 32 pi. And x=0, you substitute that in there, becomes 0 of course, so the answer is 32 pi. Have a good one.

Related Rates – Pulley Rope

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A boat is being a pulled into a dock by a rope attached to it and passing through a pulley on the dock positioned 8 feet higher than the boat.  If the rope is being pulled in at a rate of 2 meters per second, how fast is the boat approaching the dock when it is 9 meters from the dock?

Raw Transcript

Hello, everystepcalculus.com, a problem in calculus with related rates: a boat being pulled up to a dock, where the dock is higher than the boat problem. Let’s do it, you can see the problem on your screen. Index 8 to get to the menu, we gotta go up to… gonna go up on the cursor so we can go to the bottom of the alphabet to get to the R’s quicker. This is calculus 1 but also it’s in calculus one, two, and three. Related rates and we’re choosing the “Boat/Dock pull”, number 2, and we’re gonna enter our parameters. We have to press alpha before we enter anything into these entry lines here. Alpha, the height is given as alpha 8 meters, the ropes rate of change is equal to alpha 2 meters per second, it’s decreasing because it’s going closer to the Y axes. It’s pulled in, enter distance from the dock is alpha 9 meters. I always show you what you’ve entered, you can change it if you want. I say it’s okay, and I give you the perimeters, now what we’re talking about here, x equals distance from the boat from the dock and y equals the height of the dock above the boat, and L equals the length of the rope, which is the hypotenuse. And of course dL/dt is the rate of change of minus two meters per second. Given. So we find the length of the rope, which is equal to the square root of 145. Pythagorean theorem. And then we formulate the same equation basically but we work out a little bit different because we’re gonna do the derivatives of everything here. So um we do the derivatives you read all this on your paper, you do all the derivatives of the whole function before, just like this, and that’s the answer. Really the answer is square root of 145 times a minus 2 divided by 9, which is dx/dt which is the change of rate of the x axis as the boat is being pulled up the dock. And the approximate answer is -2.6759 meters per second. Have a good one.

Time Value of Money

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Time Value of Money using Calculus

$1000 present value

7% yearly interest rate over 6 years

What is the Value (future value)?

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, everystepphysics.com Problem with regard to money which I know is on a calculus test, but it’s gonna be in my menu so I can give you an example of how my programs work. So let’s do it. Index 8 to get to my menu. And we’re gonna press 2nd, and the cursor control down to… this goes page by page, so it’s a little quicker. Go down to “money”. And we’re gonna choose “money over time” and compute it over a yearly amount of time. That was the formula before. We’re going to enter the present value of the money we’re talking about. Alpha 1 thousand dollars. Interest rate, alpha 7 percent; make it a decimal, we divide by 100. And number of years, let’s choose number 6. I always show you what you’ve entered, you can change it if you want. Say it’s okay. And the value is gonna be 1521 dollars and 96 cents six years from now, based on 7 percent interest. Go to my site, well, you are on my site if you choose this menu, but subscribe so you can see other videos that I might make. Alright, have a good one. One more thing, we’re gonna go back here and just tell you one more thing. Money over time, we can also choose, you know, the number of periods, for instance, a yearly period will be 12 periods and and then semi-annual would be 2, and quarterly would be 4, so remember that if you do– and then also, you can send me a money problem if it’s not in here, I’d be glad to incorporate it in here, I like to make everything as complete as I can, so don’t be afraid to do that either, and I’ll try and program it for you. Alright, have a good one.

 

Simpsons Rule on TI89

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For more info and videos visit our Simpsons Rule master resource page.

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hello Tom from every step calculus dot com every step physics dot com problem in calculus I involving the simpson approximation system I’ll finding the area under a curve you and I’m let’s do it index eighty it to my menu I’m a scroll up to go to the s section which is simpson alphabetical Simpson’s rule there is there and we’re actually doing the integral you know a definite integral here a to be and simple way of doing it and then simpson or makes it hard n some more nonsense and now home a lotta calculations do the same thing his calculus is famous for arm surrender a function function is if the press of the freeman or anything in the central issue in my programs also for minus X square I’ll show you what you know you can change it if you want and the range given is alpha for and alpha 6 now looks pretty good we can say that’s okay in the intervals given they wanted from 6 a.m. alpha six and here’s the formula for Simpson’s rule here make the same your paper s exactly what it is you look like a genius and the change in taxes Delta X course B-minus a divided by and which is one-third and at an equal six we’re gonna do find out the X values x0 in the collection not original X is a a the 4s the lower it interval and then x1 you write notes Fort 1303 Asus computer says a less the changeover dealt actual to just computer times one at times to et cetera and we do that for the six inch wheels me play certain function turns out to be true placing me effort for into the function here -12 minus 133 over nine -1 sixty over nine -21 -2 2009 -2 53 overnight and -32 and so we’re gonna uses simpson proxy nation to to do this in a row here and that someone is this right here after me and then four times exit 12 times except you four times exit 32 times except for four times exit 5 and 5b rfb turns out to be these calculations write this on your paper
answers -1 28 over three -40 2.7 and of course you do if you do the definite integral that integrate thats exactly which can you can come up with your also pretty neat how every step calcaneus dot com go to my site by my program if you wanna past calculus and i subscribe if you want to see more videos have a good one

Trapezoidal Rule Solved on TI89

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Hello everyone this is Tom from everystepcalculus.com, everystepphysics.com. Programs that show you step by step how to do these problems. A student submitted this to Yahoo Yahoo and it was– you can see the problem, regarding the trapezoidal rule. And, let’s do it. Index 8 to get to my menu. I’m going to scroll up to get right to the bottom of the menu. Cause the trapezoidal rule, T, is closer to the W’s than the A’s. So I did it that way. There’s the trapezoidal rule there on the menu. And it’s really a trapezoidal rule calculator that’s really what would it involves, pretty neat, too. We add our function. You have to press alpha before you enter anything into these entry lines here in your calculator. Alpha X squared plus 4 times X. I always show you what you’ve entered, you can change it if you want. I say it’s okay, enter the range. The range is alpha 0 and alpha 4. Looks pretty good. Remember, that’s a definite integral, you can go to my definite integral program and do the calculation exactly. It’ll give you the same answer as what we’re gonna get here. This is a roundabout way of doing something that’s nonsense in both areas. So I say that’s okay. We’re gonna enter the intervals, which is alpha 4. And here’s the formula, change of X divided by 2, and then f(a), 2 of F of x1, 2 of F of x2, etcetera, etcetera. Down to f(b). This is the actual formula, no matter how many intervals. Change of x is B-minus a divided by n, so that’s 4 minus 0 divided by 4, turns out to be 1, and we compute the intervals.  x0, x1, x3, x4, here’s the answers: 1 and 2 and 3 and 4. and we replace them in the function. F(a) is 0, so we have 0 placed in the function, we’re substituting 0 for every X in the function. And the answer is this right here, 0. Do the same thing for f(x1) and f(x2). F(1) is placed into the function to equal 5, 12. F(x3) and f(b), so 21 and 32 answer. You’d put parenthesis around these quotation marks, the calculator makes me use quotation marks, but you’re gonna put parenthesis around these, okay, so you look good on your paper. So when we do the definite integral here you’re gonna do the trapezoidal rule approximation. There’s the approximation, and we substitute for these values here. Put this on your paper and just look like a genius. Do the calculations, comes up to this right here, that turns out to be 54 square units. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my programs if you wanna pass calculus easy, and subscribe to me if you wanna see more videos and know how my programs work so great. Have a good one.

Simpsons Rule Test Question

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Go to our Simpson’s Rule page to see more info and many more step by step video tutorials for the TI-89.

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Hello everyone, this is Tom from everystepcalculus.com, everystepphysics.com. Calculus problem regarding a Simpsons rule test question and a quad root problem. Let’s do it. Index 8 to get to my menu. I’m gonna go up to get to the bottom of the alphabet to get to the S’s, where Simpson’s rule is in my menu. At the T’s now… There’s Simpsons. Gonna enter our function. You have to press Alpha before you enter anything into these entry lines here, alpha 2 times X to the 1 divided by 4. Looks like a good function, we’re gonna enter the range, Alpha 0, Alpha 8. Intervals we’re gonna enter as alpha 8. There’s the formula for Simpson’s rule. We do the change of X first, write this on your paper you’ll look like a genius. We do the intervals all the way up to 8, just like you see it here and then we place those into the function. Write down everything you see here on your paper, and so when we do the definite integral of 0 to 8 with this function and use the Simpson’s rule for approximation, here’s what you’re putting down on your paper. Don’t slop anything off of it. And then you substitute those values we got before, you add them up, and it comes to 63.5, and you multiply times one third. Here’s the answer. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my programs, and pass calculus. Have a good one.

Graphing a parametric equation

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Hello everyone, this is Tom from everystepcalculus.com, everystepphysics.com. We’re gonna do a sketch by hand concerning parametric equations. A position formula for position vectors, and then eliminate the parameter. The parameter is T. So let’s do it. Index 8 to get to my menu. I’m already at sketch graph. Here’s the position in vector format. And you have to press alpha before you enter anything into these entry lines here. Alpha T squared minus 4, and alpha t divided by 2. If z is not given, enter 0. Alpha 0. I always show you what you’ve entered, you can change it if you want in my programs. And we’re gonna scroll down here to sketch by hand. I put in the arbitrary numbers for you that you’re gonna then work in the formula. Here’s the answer, you put these on a graph paper and you sketch the graph of this function. We’re gonna go back now and eliminate the parameter.
Of course you know how to do that, don’t you. It’s all nonsense if you ask me, calculus is nonsense. Eliminating parameter. Solve for t in the y equation, which we did here. t equals 2y, and then you put that in the x equations, into the x equation here. And here’s the answer: 4y squared minus 4. Sometimes your professor might want you to put it into a 0 format or an equal 0 format. You change, transpose, the x to the other side minus x, and then change the sign, x minus 4y squared plus 4 equals 0. Alright, pretty neat, huh? Everystepcalculus.com, go to my site, buy my program if you wanna pass calculus, and subscribe if you wanna see more videos that I might make. And don’t forget physics, either, okay? Have a good one.

Parametric Equations-Find Speed

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Find Speed

x=t^3-4*t

y=t^2+1

z=0

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Hello everyone, Tom from everystepcalculus.com, everystepphysics.com, a problem dealing with parametric equations and the item of speed. So let’s do it! Index 8 to get to my menu, go to speed. Speed is a scaler, it has no direction, no angle, unless you add time to it, which I’ll show you in my program here. There’s speed, and write all this on your paper here, the r(t) formula is x(t)i, j, and k, and x, y, and z. And we have our functions for x and y. You have to press alpha before you enter anything into these entry lines here. Alpha… the problem is T cubed minus 4 times T. And Alpha T squared plus one. Looks like the “t” is missing. Here we go, put the “t” in. Here we go, and alpha 0 for the z component, or the K component if it’s not given. These are all set up problems, they don’t happen in real life,
which is nonsense for calculus. A lot of it is like that in calculus. So, I always show you what you’ve entered, you can change it if you want. Say it’s okay. And we’re gonna scroll down here to the calculation– you have different things on the menu that you can do with this entry of “t” variables. Speed, there it is there, and of course you write the derivative of the magnitude of it, which is actually the square of the derivatives. Calculus, the sudoku of math. X prime, here’s the derivatives of that and the magnitude is then the derivative squared. I’m going to say that the time was not given in this problem at first, so to do it we’re gonna go back, we’re gonna press number 2. And so speed is the square root of 3t squared plus 2t minus 4. We’re gonna go back and do it again. Add some time component. Press yes for time… add– yes, let’s put 7 seconds. And so, it’s t equals 7, you’re entering it into the variable of the function. You’re gonna put parenthesis around this “7” on your paper but I have to use quotation marks. Turns out to be that. Turns out to be 12.5 units per second. But, because “t” is given… “t” is given, so we do have an answer, it’s 1.4732, arc tangent of the rise over run.  Have a good one, everystepcalculus.com, go to my site, buy my program if you want to pass calculus easy, or subscribe and see other videos I might make. And don’t forget about physics either. Thanks so much. Have a good one.

 

TI-89 Calculus |Radius of a Sphere

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Find the radius of a sphere. Give two points on its circumference.

Points are P=(7, -2, -6) and Q= (5, -9, 4)

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Hello everyone, Tom from everystepcalculus.com, everystepphysics.com. We’re gonna do a calculus three problem regarding a sphere. And we’re given two points on it’s circumference. Outer shell, you know. And let’s do it. Index 8 to get to my menu,
find the radius. Scroll up to get to the bottom of the alphabet, cause the sphere radius is in the S’s and closer to the W’s than the A’s. There’s sphere radius there. Choose that one. We’re gonna put our points in.You have to press alpha first. Alpha 7, Alpha minus 2. Alpha minus 6. Alpha 5 Alpha minus 9. Alpha 4. I always show you what you’ve entered, you can change it if you want. Looks okay. Now I’m gonna find the radius number 4. Here’s the formula. Write this stuff on your paper. And R equals these calculations here, just as if you did it yourself without mistakes. And the answer. Pretty neat, huh? Everystepcalculus.com, go to my site, buy my programs if you want to pass calculus, and subscribe if you want to see more videos from me. Have a good one.

Find the Standard Equation of a Sphere

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Find the standard equation of the sphere.

Let P1 = (-7, -9, 7) and P2 = (0, 1, 1) be endpoints of a diameter

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Hello everyone, Tom from everystepcalculus.com, everystepphysics.com. A problem regarding a sphere and the standard equation a person submitted, and let me show you how I do it in my programs. Index 8 to get to my menu, my main menu. I’m gonna scroll up to get to the S’s at the bottom, it goes to the bottom of the alphabet so it’s easier and quicker to get there. You can press second and these cursors to go screen by screen on your calculator. Those are all the choices you have, and we’re gonna have sphere equation.
And we’re gonna enter our P, Q points. All professors do things different, which I’m against in calculus. Well, I’m not too thrilled about calculus at all. We have p1 and p2 here, in most cases it’s P and Q points. You have to press alpha before you enter anything in these entry lines here. Alpha, the first one is minus 7. There it is. Alpha minus 9. 7 is the P point. These are point on the outside of a sphere, and they give you two points are you’re supposed to find the radius. And different types of things. Not easy. Even if you know the formula it is not easy, you’re gonna mess up on the minus signs or whatever. That’s why the program steps up so you don’t mess up, and I didn’t mess up. The Q point is Alpha 0, Alpha 1. Alpha 1 for the Z point. I always show you what you’ve entered you can change it if you want. I say it looks pretty good. And we’re gonna choose equation, standard equation, number 5. There’s the formula. And you have to find the xo, yo, zo first Which is this system here. That equals this. Standard equation that is these entered into the equation. Here’s the standard equation. Pretty neat, huh? Everystepcalculus.com. Now I noticed, with the minus in minus, you might have to think in life a little bit, so you might have to say, oh there’s a minus and minus, minus times a minus is a plus. So you might put on your paper, x plus 7, over 2. Or same thing with y. Y equals minus, minus a minus, which is equal to a plus. Which would be y plus 4, and this would be z plus 4. So, keep that in mind. Have a good one. Everystepcalculus.com, go to my site, buy my program if you want to pass calculus. Subscribe if you want to see more movies from me. Thanks and have a good one.

Vector Function on TI-89 & Titanium

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Hello everyone, Tom from everystepcalculus.com everystepphysics.com, a quick example of
vector valued function, r(t) formula, or vector function. And with regard to speed. So, let’s do it. Index 8 to get to my menu. We’re gonna scroll up to get to the bottom of the menu so that we’re closer to the s section; it’s all alphabetical. I choose speed. Speed is a scaler, meaning it has no direction, it has magnitude, but no direction. Unless time is added to it, and then it does have a direction. You’re gonna enter these values here, but if Z is not given you’re gonna enter 0, okay? So, you have to press alpha before you enter anything in these entry lines here. Alpha minus 3 times T Alpha 2 times T Alpha minus 6 times T. I always show you what you’ve entered, you can change it if you want. There’s the vector. These indicate that it’s a vector, these arrows here. Say it’s okay. Now we’re gonna choose speed, we’re looking for speed. It’s right there. And it’s given by the magnitude. Magnitude is the derivative of the function times the squares of each one of them. So it’s X prime of t squared, y prime of t squared, z prime of t squared. And the derivatives are minus 3, 2, and minus 6. And we square them. Asks if there’s time given, I’d say there’s no time given in this one. So we’re gonna choose number 2. And then just square the values, sum them up,
49, and there’s the answer: 7 units per second. Pretty neat, huh? everystepcalculus.com, go to my site, buy my programs, and subscribe if you want to see other videos. Have a good one.

Find Midpoint of Sphere on TI-89

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Find the midpoint of a sphere.

Let P = )5, -2, 3) and Q = (0, 4, -3) the endpoints on the circumference sphere.

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Hello again everybody this is Tom from everystepcalculus.com, everystepphysics.com.
We’re gonna do some calculations in a sphere. This is generally calculus three. And we’re gonna find the midpoint, or center, of a sphere. Index 8 to get to my menu. You can scroll up to get to the bottom of the menu so you can get to the S section quicker. You can press second and the cursor here to get screen by screen instead of one click like I’m doing. This is a simulator. Now we’re gonna choose here, center and midpoint. We’re gonna enter our P and Q points pressing Alpha first. Alpha 5. minus 2 Alpha 3 The Q point is Alpha 0, Alpha 4
Alpha minus 3. Now we gotta go back and change them. Alpha 5 Alpha minus 2 Alpha 3 Alpha 0 Alpha 4. And Alpha minus 3. I always show you what you’ve entered, you can change it if you want, which we just did. Say it’s okay. Now I’m gonna press number 1. Number 3 for midpoint Here’s the calculations: xo, yo, zo. And the answer. Everystepcalculus.com, go to my site buy my programs if you want to pass calculus.
And also subscribe so you can see other videos I might make. Hey have a good one.