4. Use Taylor series expansions to compute the following limits: sin(x) - x + (a) lim x-0 x cos(x) - 1+ (b) lim - arctan(x) - x x-+0 23 (c) lim In(1 + x) - sin(x) + 2 x-+0 (1+ 2 n (d) lim . (HINT: First compute the limit of In of this expression). NOTE: In (c) and (d), you will need the Taylor expansion ron In(1 + x) = x N E 3 n=1 valid for Ja|