Taylor Theorem - Calculus - Solved Exam, Exams of Calculus

Download Taylor Theorem - Calculus - Solved Exam and more Exams Calculus in PDF only on Docsity!

C Math 106 BC Exam 02 page 1 11/05/2010 Name. Ssestel soln ‘+ 1. Let f(z) = (Vz —1)* = (a — 1)9/2. la. Use the following table of derivatives of f to find the third degree Taylor polynomial approximation P3(xr) of f(x), in powers of x — 5, ie. a = 5. We need cKS’ ¢ FR) CK =U C20 Isfu 2 IF o> a = Se. = Cs Bo Bh => P(x)=30+20{%-s)+ Flies)" Els) 1b. Taylor’s theorem guarantees that f and P3 will separate by no more than what value (call it €), on the interval [2.5, 6]? Show all your work. (Find Ky to two decimal places. Find the maximum guaranteed error € to 4 decimal places.) | £(X)- P&I! £ €= Kolcal Aes \f ™(x) < Ky On (ee, c] Gi phicel analy as dank tba inp He smbbst Ky te 10 ahohmel alates O,S2 OsL ]x-s| occon ak XE 25 ee Goo, he mon f , 0.84 _ OS2725 go E = CFE ze OBIE a : J eroop = | (x=) A] 1c. Since f(x) = (V¥x—1)°, we could use it to find (/3)° = 3°/? by taking x = 4. Use the same x to approximate (V3)° with your Taylor polynomial P3(x). What do you get? What’s the error in this approximation? (Write your answers to 4 decimal places). by caleslator, 3 h os = (5. 5885~ and F(4 ‘Je fissaas] He dhfermee. 5 le 0. 0052 |