Calculating 13th Taylor Coefficient of f(x)=e^(7x) at x=3

[cathy]

Homework Statement

Determine its 13^{th} Taylor coefficient of the Taylor Series generated by f at x = 3.
f(x)=e^(7x)

Homework Equations

I used the fact that the series for e^x was ∑x^n/n!

The Attempt at a Solution

Using that above, and replacing x with 7x, shouldn't my answer be 3x*7^13/13!
But that is incorrect? Please advise where I am going wrong? Thank you

 

[LCKurtz]

Homework Statement

Determine its 13^{th} Taylor coefficient of the Taylor Series generated by f at x = 3.
f(x)=e^(7x)

Homework Equations

I used the fact that the series for e^x was ∑x^n/n!

The Attempt at a Solution

Using that above, and replacing x with 7x, shouldn't my answer be 3x*7^13/13!
But that is incorrect? Please advise where I am going wrong? Thank you

Here's a few questions for you. If$$
f(x) = \sum_{n=0}^\infty \frac{ f^{(n)}(3)}{n!}(x-3)^n$$what value of $n$ gives the 13th term? Once you have that, what is that many derivatives of $e^{7x}$ and what do you get when you evaluate that at $x=3$?

 

[cathy]

Here's a few questions for you. If$$
f(x) = \sum_{n=0}^\infty \frac{ f^{(n)}(3)}{n!}(x-3)^n$$what value of $n$ gives the 13th term? Once you have that, what is that many derivatives of $e^{7x}$ and what do you get when you evaluate that at $x=3$?

Isn't it the 13th value of n that gives the 13th term?

 

[LCKurtz]

No. Give it some thought. Write out some terms.