Show us what you got when you did the substitution. That's the right approach.Minjie said:Homework Statement
Let f(x)=cos(x^5). By considering the Taylor series for f around 0, compute f^(90)(0).
by the way, I don't know how super/sub script works?
Homework Equations
The Attempt at a Solution
I tried to substitute x^5 into x's Taylor Series form and solve for f^(90)(0), but it gave me a wrong answer.
Nothing changes in that part. In your formula above, replace x by x5. That will be your Taylor series for cos(x5).Minjie said:cosx=∑(-1)^n/(2n)!*x^2n
I am not sure what the an part: (-1)^n/(2n)! will becomes when I substitute x5 into the series.
A Taylor series is a mathematical representation of a function as an infinite sum of terms, where each term is a derivative of the function evaluated at a specific point.
Taylor series allow us to approximate complex functions with simpler ones, making it easier to analyze and solve problems in various fields such as physics, engineering, and economics.
The main purpose of using a Taylor series is to approximate a function at a specific point, which can be useful in solving problems where the function is difficult to evaluate directly.
The coefficients of a Taylor series can be found by taking successive derivatives of the function at the point of expansion and evaluating them at that point.
No, a Taylor series can only represent analytic functions, which are functions that can be expressed as a power series. Functions with discontinuities or vertical asymptotes cannot be represented by a Taylor series.