Use the Taylor polynomial of degree up to 3 for y = cos x along with Taylor's inequality to estimate (integral from 0 to 1) of cos(x^2) and give a bound on the error that your estimate makes.
I'm not quite sure how to do this.
Printable View
Use the Taylor polynomial of degree up to 3 for y = cos x along with Taylor's inequality to estimate (integral from 0 to 1) of cos(x^2) and give a bound on the error that your estimate makes.
I'm not quite sure how to do this.
Also, you need to find the remainder term to find the bound on error. You know...
Ok thank you, I don't know why the integral threw me off...seems straight forward enough :).
Incase anyone else is interested in this answer in the future, the x^8 term should not be included (since it is of degree 3 and the x^4 term isn't used). Thanks again for the reply though.
Yes, this is correct. Note that if you wantto
use the
order expansion, which is what I implied with
I've edited the post to show we are finding an