Question

Find T5(a): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = T5(x) = Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.001774 of the right answer. Assume for simplicity that we limit ourselves to a < 1.

Answer 1

Jacmate liste Daha Page digret's' Given that tenga cosa ath We know that, Taylor's theorm, fond I ca) + n-a) 31 (a) tn-a? 11 2 + n-a3 t cast +(n-a) n 0 From frog tgp 7 - sina f'(o) zo I" (x) ftoget Z Cosa f (n) z sinn 0) = firm = cosa Pinco) 27 f"ena = -sinn to)zo

le Det Pone have to gind polynomial of digree's then core fix to tan +6) + 2 f cooth +29 41 + to pivco) + 25 + 10) 31 5! Putting the valuess get, IT, EN) z fon) 1 tk.0+ 22 21 43 . & no 15 Tg ang 1 + 42 23 + + 500 I It H2 2 + Zo Am From equation o It 2 21 + 23 + ne cos (6.001774) t na 73 + 2 4

oz|18190-0) all 15 spttt1º5-2) .0 5 |(9100.07ky! thin 02 (2) gt 0 = (0) gt kurse 2 (Rdgt 8 is staaten (77573(texto-os hat i(Hp 1o-ul (2) it IR (6:06188 L azo n=4 nz 6.00 1774 from an o i(Hw tot) (2) (414 cutoton erpurourt torto tout nout Date