💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

WZ
Numerade Educator

Like

Report

Problem 19 Medium Difficulty

Find the Taylor series for $ f(x) $ centered at the given value of $ a. $ [Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0.$] Also find the associated radius of convergence.

$ f(x) = x^5 + 2x^3 + x, $ $a = 2 $

Answer

$f(x)=50+105(x-2)+92(x-2)^{2}+42(x-2)^{3}+10(x-2)^{4}+(x-2)^{5},$ $R=\infty$

Discussion

You must be signed in to discuss.

Video Transcript

two problem is finding a tiller, Siri's or of Blacks center that has given one off, eh? I also find that the certainties videos of Emergence after Wax is he got axed too far for us to Sam's Ex Cuba plus tax. And it's true, the first two behalf after two. It's the call to lefty and half from is a good Father axe to or plus six X squared plus war. So from true True one, Home Secondary motive is equal to one p x cube, plus twelve bucks. Second two at this point to is the co two one and four third derivative equal to sixty Ex choir stall from front from as Want to. It's a cultural too far, too Fourth derivative, it's equal to one hundred and twenty X, So fourth derivative at this point actually got to and say hello to two four zero on DH Fifth Renter. And so you go to one hundred and twelve and after Conservative is equal to zero. If N is pretty far, then we have the killer theories for after Max iss, some from zero to infinity, uh, and derivative at this point two over factorial times X minus two is a part ofthe end, which is the cultural fifty plus one x minus two plus mine t two times x months to score, plus forty two times X plants two to the power of three plus and camps X minus two. The problem for us. Smile minus two to public foward, please Taylor Siri's for half a box is upon nominal, so it's converted every wire. The readers of Emergence is infinity.