I'm having trouble with a few homework problems, so here are the problems and my thoughts.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Use the power series to evaluate the function

[tex] f(x)= \frac{1}{\sqrt{1+x^4}}-cos(x^2)[/tex]

at x=0.01. Use the first two terms in the series to approximate the function, but estimate the error introduced by truncating the series.

The attempt at a solution

My main problem with this question is that it appears the function is equal to zero at, and in the neighborhood of, x=0. Also, the values of all the derivatives of the function are zero at x=0, so my power series expansion looks like this: f(x)=0. Am I missing something here, or is this really a "trick" question?

2. The problem statement, all variables and given/known data

Find a two term approximation and an error bound for the integral

[tex]\int_0^t e^{-x^2}dx[/tex]

in the interval 0<t<0.1

The attempt at a solution

I'm not sure how to start this one...should I treat the integrand as the function or is the integral included? If the function is just the integrand, I don't see any problems. However, if the integral is included in the function then how would I proceed?

Any thoughts or hints you all could provide would be most appreciated. This HW is due tomorrow so quick replies are welcome!

Josh

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# Homework Help: Power series applications

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