Question

Please Help! Use the first three non-zero terms of the maclaurin series to approximate the value of the definite interval from 0 to 0.8 (1-cost)/t^2 d

Answer 1

i could have sworn we did this. was it wrong?

Answer 2

It was, I might of scrwed up the last part

Answer 3

when we got to 1/2 - x^2/24 + x^4/720, I mustve screwed up after

Answer 4

i recall the series was
\[\frac{1}{2}-\frac{x^2}{24}+\frac{x^4}{720}\] plus stuff hold on let me check

Answer 5

http://www.wolframalpha.com/input/?i=mclauren+%281-cos%28x%29%29%2Fx^2
yup that part is right

Answer 6

And then I probably screwed up with the integrating by term part

Answer 7

technology gives me .39298
http://www.wolframalpha.com/input/?i=integral+0+to+.8+%281%2F2-x^2%2F24%2Bx^4%2F720%29

Answer 8

might as well use it because you are not going to compute this with .8 without using a calculator, but the anti - derivative should be straightforward since you have a polynomial

Answer 9

That's actually what ! got, when integrating by term I got sqrtx - x^3/450 + x^5/1440 .. is that good?

Answer 10

However it also asks to do a test to see if it converges, and the ratio test doesn't work when I use that

Answer 11

where id the root x come from?

Answer 12

anti derivative of \(\frac{1}{2}\) is \(\frac{x}{2}\)

Answer 13

Why do I have to take the anti-derivative if I can evaluate the integral before I take it?

Answer 14

second question is also confusing. what does it mean "converge" when you only have three terms? unless you take the infinite series, you have a polynomial.
the infinite series will of course converge but you will have write a formula for it

Answer 15

you lost me on the last question
your job is to find the definite integral right? a number

Answer 16

I think I do have to write a formula for it, and I have to clue as to how to go from an integral to a series formula

Answer 17

in other words
\[\int_0^{.8}\frac{1}{2}-\frac{x^2}{24}+\frac{x^4}{720}dx\]

Answer 18

to find this integral without using wolfram you need an anti derivative of
\[\frac{1}{2}-\frac{x^2}{24}+\frac{x^4}{720}\]

Answer 19

Yup that's right, kk I got that

Answer 20

that is
\[\frac{x}{2}-\frac{x^3}{72}+\frac{x^5}{3600}\] if my arithmetic is right

Answer 21

the replace x by .8 and see what you get

Answer 22

i gotta run, but post the question about convergence again, that is about convergence of the anti derivative. believe me it converges everywhere because you have a factorial in the denominator

Answer 23

Thanks!!