Let f(a:) =2 2m + mln(a:) . (a) Find the linear approximation of the function around a: = 1 . (b) Use the Iinearization from part (a) to estimate the value of the function at a: = 1.05. (cl Find the second degree Taylor polynomial T2 (3:) of the function f(r1:) = 233 + a: ln(:c) centered at :19 = 1. (d) Use the fact that f(a:) m T2 (ac) to find an approximated value of the integra 1 1 Hint: f(m)d:1: % / T2 (:13) d3}. Round your answer to four decimal place . 0.5 (e) Evaluate the integral 1 / 250+:131nmdw 0 .5 Round your answer to four decimal places