Question

12. [-16 Points] DETAILS LARCALC11 9.7.051. Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = sin(x), approximate f(0.6) Need Help? Read It Watch It Talk to a Tutor 13. [-15 Points] DETAILS LARCALC11 9.7.053. Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = e, approximate f(0.9) Need Help? Read It Talk to a Tutor

Answer 1

through Containg GER 2 f(x)=f(ut fw t-t (12) <Pb> given function f(n= sinne , approximate floo) indicated value of a to be less than 0.001 soli- Let f is a real valued function which is Sinco.6) = Pocob) + Ro(0.6) differentiable ntl order in the interval f'(c) (n-1) + 8-C) 2) f(c) x 5 + Roln) where Rachl= fenti) (nt), intl DE) (Z) (nti) t'(n) = tcosx -Sinn - CosR (al fm = Pain't Rocx) nti (n-ight max Lot us take fcn) = sinn - if(n)

n such that we need to find I Rocnol < 0001 R0.6) (0.00) Rain & htt) Coght | infoCounty.com ntl (0.6) (nti) (0.6) 0.36 0.36 = 0.18 21 (0:0) 0.216 E 0.036 2 31 6 3 (06) + 0.1296 = 0.0054 41 24 4 (0-675 0.07776 120 0.000648 5) cooool (R4(0-6), co - least degree Polynomial (n=4