Hello, Tom from everystepcalculuseverystepphysic.com. Maclaurin series, let me show you how to do that in my programs, index 8 to get to the menu the main menu I’m going to scroll down to Maclaurin series and you can go on your calendar second and get through the alphabet quick where you want to go to I’m just going to scroll down here because the simulator sometimes screws up if you do that, so I’m to choose Maclaurin series, Maclaurin series is when your center is 0 (a) is 0 and Taylor series you have great than 0, here is the formula for Maclaurin series [f^n(0)*x^n]/ n! You should always write formulas on your paper you will get couple extra points and remember calculous is always good and partial credits on the class curves and you can get more than the person sitting next to you then you pass that class and that’s all we are interested in passing it not learning nothing, the Taylor series formula, we are going to enter the function we have to press alpha before you enter anything in these entry lines here so we are going to press alpha the function is alpha x* yellow button on then equal sign for e, (e) is a minus x and then we are going to put 0 in for the Maclaurin because that’s what we are doing finding the Maclaurin series and the we are going to have to press alpha again, alpha 0 and it’s going to show you what you have entered and you can change it if you want that’s if it isn’t right, we write this formula on our paper right? We are going to do that, we do the first 5 derivatives of that function which is here then we take those derivatives and we set it as to equal to zero, enter zero in for x and we come up with this an we take those answer’s and divide it by the factorials of 1,2,3,4,5 which turn out to be these answer’s 1,-1, 1/2, -1/6, 1/24 and we enter those answer’s into the formula here (x-0) to the 1,2,3,4,5 powers and here is the answer f(x)=0 don’t forget that 0 plus x plus minus x squared plus x cubed over 2 plus minus x to the 4/6 etc.etc. pretty neat huh everywhere is.com don’t try to pass calculous without these programs go to my site buy them enjoy passing calculous, okay calculous should only be taught to math majors not to us but since they do that we need to do anything we can to pass it and get out of there hey have a good one.

## Maclaurin Series, 1/(1-x)

Hello again everybody Tom from everystepcalculus.com and everystepphysics.com. Maclaurin series and other functions that I want to do comes up on the Yahoo answers problems students having trouble with it so let’s deal with these programs. Index 8 to get to my menu, scroll down to Maclaurin series there is it there then press enter you notice the difference between Taylor series and Maclaurin is if you use zero for the (a) which is the center point to do the series and this is the formula from Maclaurin series and here is the Taylor series formula now we are going to enter the function and we have to press alpha before we enter anything in these entry lines here and the function is alpha 1/(1-x) and because it’s Maclaurin we are going to put 0 in for (a) here, alpha 0, we could put the -1 here but that’s not what I entered let’s leave it and see what’s happening here I say it’s okay then, again write the Maclaurin series on your paper and you will get credit couple points you know because you partial credits in class curves so you don’t need to be a genius at this stuff just get a few more points than the turkey sitting next to you, and we do the derivatives here the first 5 derivatives equal this 120/(×-1)^6 and set that and put 0 in for x and we come up with 120, we take those answer’s and we divide it by the factorials of 1,2,3,4,5 and come up with all 1’s put all 1’s in here and multiplying it times x-0 to the powers of theses here and the answer is 1+x+x^2+x^3+x^4+x^5 that’s the answer. Go to my site buy my programs and enjoy passing calculous it’s a tough course and you have a good one.

## Maclauren Series Solved on the TI-89

### Raw Transcript

Hello again this is Tom from everystepcalculus.com and I’m going to do a Maclauren Series for you at sin(x) right now. Let’s get started you enter i_n_d_e_x and 9 in here and you get my menu comes with instructions when you buy my programs um..press enter here and we’re gonna scroll to Taylor and Maclauren in the menu. Here’s Maclauren series formula n is the number of derivatives you’re taking I’ve stopped it at five in these programs and a is the point and a function where you’re going to approximate the slope of a line running into the function alpha sine of two times X and add zero cuz we doing the Maclauren series Alpha zero, show you what you’ve entered,you can change it if you want I show you the formula for Maclauren series and we do the computations this is the first five

derivatives inside 2x and then were gonna put zero in here for x and we’ll work the derivatives with that here are the answers here write all this on your paper we’re going to use the factorials here

of what we just computed and these are the answers here and you write this on your paper all very important exactly accurate and here’s the answer 2 of x 0 -4x cubed o 4×5 over 15 pretty neat huh… everystepcalculus.com. Go to my site by my programs and pass calculus don’t forget to subscribe to the site so that you can see other programs that I design and blogs