# Math Help - Using the degree six Taylor polynomial approximate the value of f(1).

1. ## Using the degree six Taylor polynomial approximate the value of f(1).

We know that e^x = n=0, infinite (x^n)/n!. Using this knowledge find the power series of the function f(x)=(e^x + e^-x)/2. Using the degree six Taylor polynomial approximate the value of f(1).

2. Originally Posted by ewkimchi
We know that e^x = n=0, infinite (x^n)/n!. Using this knowledge find the power series of the function f(x)=(e^x + e^-x)/2. Using the degree six Taylor polynomial approximate the value of f(1).
So where are you stuck?

Replace $x$ with $-x$ and you have the Taylor series for $e^{-x}$.

Then substitute the two series into $f(x)$ and simplify...

3. ## Did I get it right?

After integration, I got x + (x^3)/6 + (x^5)/120 + (x^7)/5040

I plugged in 1 and got

5923/5040.

Is that right?