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whatcha got so far?

didn't do it yet im doing it now i just did the first problem which was cos(x)

wouldnt x=0 be a Maclaurin series?

as well as the answer

Maclaurin series is just s special case of taylor series when it's centered at 0.

cos(0) -sin(0)-cos(0)+sin(0)+cos(0)....like that rght?

forgot the factorials....

cos(x^2) = 1- sin(0)x -cos(0)x^2+sin(0)x^3+cos(0)x^4
-------- -------- --------...
2! 3! 4!

right?

x^2...x^4....x^6....

i believe so

i havent finished yet

i got no idea what to do after that :)

Do you know how to find the Taylor series of cos x at x=0?

yes i did alread

here

Good. So, I just used that expansion and replaced x by x^2.

F^(1) (x^2)=-sin x^2?

f2 = -cosx^2?

What's that?

derivatives of the function

of cos(x^2)?

then your evaluate them then move on to the generate a formul

part

kk i didnt know that

And for the second derivative, you should apply both the product rule and chain rule.

kk sec....... im going to try to do it now and thanks for this your a life saver

what did you get for the second derivative

-4x^2cos(x^2)-2sin(x^2)

the third derivative

and you said the fourth derivative should be the one that isnt zero when evaluating it right?

ok explain to me why it really doesnt matter to find the derivatives

that is if you can

yes
so the ans should be
1-1/2x^4+1/24x^8 then whats the nxt one

-x^12/720

is there any tricks to getting the correct answere fast4r then going through each an evaluating it

because after you find this i must know if it converges or diverges

oh ok

can you help me figure out if it now converges or diverges?

You know how to use the ratio test?

is there an easy way to know it so i know? or no

because i dont understand exactly bc my professor did a poor job explaining it

is that*

like ive got the definitions i front of me but explain why it converges or diverges

ill talk to you on the other page this one i need for this page