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).

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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).

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So where are you stuck?

Replace with and you have the Taylor series for .


Then substitute the two series into and simplify...

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?