Question

So the formula for taylor series is ___, and how about 1/x^3?

Answer 1

\[\color{blue}{y=f(x)~~~{\rm at~~x=a~~is~given~by~}~~\sum^{\infty}_{n=0}\frac{f^{(n)}(a)}{n!}(x-a)}\]

Answer 2

so what's the how about for?

Answer 3

I will try to do 1/x^3 at x=1

Answer 4

ah, ok, so first, find some derivatives

Answer 5

f(x)=1/x^3 f(1)=1
f'(x)=-3/x^4 f'(1)=-3
f''(x)=24/x^5 f''(1)=24
f'''(x)=-120/x^6 f'''(1)=-120

Answer 6

how'd you get 24?

Answer 7

check your second derivative

Answer 8

-yeah, my bad it is 12, and then -60

Answer 9

that twould be correct

Answer 10

and what do I do after ?

Answer 11

plug and chug

Answer 12

a=1

Answer 13

then there is a remainder theorem for the remaining

Answer 14

but you just need to find the limit if I understand

Answer 15

I think I am too weak for taylor series... not that I ever was good at math.
I will review easier examples first and then do this one.

Answer 16

tnx for your input

Answer 17

wait, you've already done all the work

Answer 18

\[\color{blue}{y=f(x)~~~{\rm at~~x=a~~is~given~by~}~~\sum^{\infty}_{n=0}\frac{f^{(n)}(a)}{n!}(x-a)^{\color{red}{n}}}\]

Answer 19

\[ \sum^{\infty}_{n=0} \frac{f^{(n)}(a)}{n!}(x-a)=f(1)+f'(1)/1! *(x-1)+f"(1)/2!*(x-1)^2+...\ \]

Answer 20

yea, forgot to toss in the exponent, sorry

Answer 21

then I am pretty stupid that I can't plug it in, do I get?
\[=1+\frac{(-3)}{1!}(x-1)+\frac{(12)}{2!}(x-1)^2+\frac{(-60)}{3!}(x-1)^3+\frac{(360)}{4!}(x-1)^4+...\]

Answer 22

yea, that's all there is to it, just simplify

Answer 23

\[+\frac{(360)}{4!}(x-1)^4+\frac{-360 \times -7}{5!}(x-1)^5+....\]

Answer 24

then they like to use a remainder theorem

Answer 25

usually they will say what power they want this in

Answer 26

I haven't learned that yet. My teacher said the he doesn't consider it very important.

Answer 27

Well, if it won't be a pain I can look it up and learn it....

Answer 28

it's not crazy important, but you just did it

Answer 29

I just did the remainder theory ?

Answer 30

anyway... I will worry about it later. I need to comprehend the task of writing the taylor series (which is not as crazy as i though it was).

Answer 31

tnx again.


CLOSED

Answer 32

np

Answer 33

for your reference http://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx