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

• Jun 2nd 2010, 12:09 AM
ewkimchi
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).
• Jun 2nd 2010, 12:32 AM
Prove It
Quote:

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

Then substitute the two series into \$\displaystyle f(x)\$ and simplify...
• Jun 2nd 2010, 09:48 AM
ewkimchi
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?