Find Degree 3 Taylor Polynomial Approximation of 5ln(sec(x))

[hahaha158]

Homework Statement

Find the degree 3 Taylor polynomial approximation to the function f(x)=5ln(sec(x)) about x=0.

Homework Equations

the taylor polynomial equation

The Attempt at a Solution

Here are my derivatives
f(x)=5ln(secx)
f'(x)=5tanx
f''(x)5sec^2(x)
f'''(x)=10sec^2(x)tanx

Please let me know if any of the above are wrong

When I try to plug in 0 for the x's above I end up with a whole lot of undefined answers because sec0=undefined. How can I get around this?

thanks

 

[Fightfish]

Are you sure that $sec 0 = \frac{1}{cos 0}$ is undefined?

 

[hahaha158]

Are you sure that $sec 0 = \frac{1}{cos 0}$ is undefined?

oops, got sec and csc confused. Thanks