Question

TAYLOR SERIES PROBLEM HELP

Answer 1

Let f be the function given by f(x) = integral of cos*sqrt of t dt, from 0 to x, x greater than equal to 0. Which of the following is the taylor series of f about x =0

Answer 2

\[\int\limits_{0}^{X}\cos \sqrt{t} dt, x \ge 0\]

Answer 3

THAT IS THE FUNTION

Answer 4

a) 1 - (x/2) + (x^2/24) - (x^3/720)....
b) x + (x^2/3) + (x^4/15) + (x^5/105)...
c) x - (x^2/2) + (x^4/6) - (x^6/24)...
D) x - (x^2/4) + (x^3/4) - (x^4/2880)...

Answer 5

can't you use the expansion of cos(u) and substitute x^(1/2) whenever u appears?

Answer 6

I want to know how to get the answer, not only what the asnwer is if u dont mind

Answer 7

i know taht cos(x) = x - (x^2/2) + (x^4/4) - (x^6/6).... but idk what to do after

Answer 8

so can't you substitute x^(1/2) for every x in the expansion of cos(x)?

Answer 9

let me try

Answer 10

i have teh answet key and the asnwer is D but im not sure if substituing x^1/2 is how they got taht answer....

Answer 11

i tried but i get x - (x/2) + (x^2/4)....

Answer 12

tahts wat i get when i substtue x^1/2

Answer 13

do u see how they got D as an asnwer

Answer 14

WAIT D) NEEDS a correction it should be : x - (x^2/4) + (x^3/720 - (x^4/2880)

Answer 15

are u there?

Answer 16

i'm not so sure anymore, you can try it doing a straight differentiation as well

Answer 17

how? what do u get

Answer 18

int(1 + f'(0)x + f''(0)x^2/2! + ...)