0 X D2L Dropbox Folders - N X D2L Homepage - MATH X 7- Crowdmark X C (a) Find The Degree X & WA_8.pdf X WA 8.pdf X *MATH 119 : CALCUL X + C O X(+ | C:/Users/zhiqi/Desktop/WA_8.pdf Z 1:: AZZA @ BE M Gmail @ A Private Summer... 1013 0 7 YouTube Minuti y! what is radius of.. PostLab 4.docx WA_8.pdf 1 / 1 125% + (cer (d) 1- 3. (3+2+3 points) Compute each of the following Taylor polynomials of degree 3 centered at the given point, and write it in the standard form given in the lecture notes: (a) sin(x) at To = (b) e3 at To = 0 (c) x3 - 8 at To = 2 4. (2+2 points) (a) Use Taylor's Inequality to bound the error in using the Taylor polynomial from 3(a) to estimate sin( 2) (you may keep 7 in your answer). (b) You may notice that your error is still fairly large, since " is pretty far from 5. Suppose we wish to use a larger Taylor polynomial: what is the smallest n so that approximative sin(# ) using the degree n Taylor polynomial of sin centered at { gives a guaranteed error of less than 100% by Taylor's Inequality? Note: you may use a 4-function calculator for this part (approximationg 7 by 3.14 will be close enough for this purpose). Trial-and-error will work pretty quickly if your setup is correct. 5. (5 points) Use a Taylor polynomial with four nonzero terms centered at 0 to approximate the value of 3 arctan(x) do. Give your answer rounded to 3 decimal places. (Hint: it will help to recall that di arctan(x) = 2. Which of the answers from Question 2 could help here?) O 3:51 PM 2022-03-16