Question

find the Taylor series about the indicated center
and determine the interval of convergence.

Answer 1

f (x) = e^(x−1), c = 1

Answer 2

This series is described by\[f(x)=\sum_{n=0}^{\infty}\frac{ f^{(n)}(1) }{ n! }(x-1)^n\]Now let's see if you can find the derivatives...

Answer 3

Looking at f(x)=e^(x-1), it is clear that \[f(x)=f'(x)=f''(x)=f^{(n)}(x)\]so all the derivatives in x=1 are e^0=1
The Taylor series becomes:\[e^{x-1}=\sum_{n=0}^{\infty}\frac{ (x-1)^n }{ n! }\]What about the radius of convergence?

Answer 4

@ASAAD123: do you copy?