# Calculus II Homework Problem

• Apr 4th 2010, 04:56 PM
colonelone
Calculus II Homework Problem
Not sure how to do this one, the way that it is worded confuses me. I'd appreciate any help you may offer.

Find an approximation for h(x)=e^(-x^2)) by finding a formula f(x) = e^x = p5(x), where p5(x) is a fifth degree polynomial, and by writing h(x) = f(-x^2) = p5(-x^2).

Thank you
• Apr 4th 2010, 05:00 PM
skeeter
Quote:

Originally Posted by colonelone
Not sure how to do this one, the way that it is worded confuses me. I'd appreciate any help you may offer.

Find an approximation for h(x)=e^(-x^2)) by finding a formula f(x) = e^x = p5(x), where p5(x) is a fifth degree polynomial, and by writing h(x) = f(-x^2) = p5(-x^2).

Thank you

$\displaystyle e^u = 1 + u + \frac{u^2}{2!} + \frac{u^3}{3!} + ...$

now find the desired polynomial approximation of $\displaystyle e^{-x^2}$
• Apr 4th 2010, 05:15 PM
colonelone
Quote:

Originally Posted by skeeter

$\displaystyle e^u = 1 + u + \frac{u^2}{2!} + \frac{u^3}{3!} + ...$

now find the desired polynomial approximation of $\displaystyle e^{-x^2}$

Where u = $\displaystyle {-x^2}$?
• Apr 4th 2010, 05:22 PM
skeeter
Quote:

Originally Posted by colonelone
Where u = $\displaystyle {-x^2}$?

that's how it works