I'm doing some review over summer before starting college, and one of the practice exams has a question pertaining to the remainder of a taylor series(adsbygoogle = window.adsbygoogle || []).push({});

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

Show that [tex]\left|\cos{(1+x)}-\{\cos{(1)}(1-\frac{x^2}{2})-\sin{(1)}(x-\frac{x^3}{3!})\}\right|<\frac{1}{15000}[/tex] for [tex]|x|<0.2[/tex]

2. Relevant equations

The two equations I somewhat remember are

[tex]R_n(x)=\frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{(n+1)}[/tex]

and

[tex]|R_n(x)|\leq{}M_n\frac{r^{n+1}}{(n+1)!}[/tex]

where M (iirc) is the largest value of the nth derivative in the area of convergence?

3. The attempt at a solution

Here's where I'm stuck; my class in high school never fully went over error of taylor approximation because it wasn't part of the curriculum, so we were given the equations without any actual application. To make matters worse, I last took AP calculus BC over a year ago, so this is still very rusty. Can anyone point me in the right direction?

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# Homework Help: Taylor Series and error

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