Proof of Taylor's series

neptune said:

Hello folks,

I was studying Taylor's series,
Question 1: but i don't know how they got the formula for Taylor series

books always starts with the power series of

but why ?

Definition :" Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial. " (source - wikipedia)
Question 2: what is k times differentiable.

Click to expand...

neptune said:

Hello folks,

I was studying Taylor's series,
Question 1: but i don't know how they got the formula for Taylor series

books always starts with the power series of

but why ?

Definition :" Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial. " (source - wikipedia)
Question 2: what is k times differentiable.

Click to expand...

ESDR said:

hello,
I have also studied the taylor theorem but don't understand the practical application where it is seen?

Click to expand...