(16) (Bonus) A piece of wire 100 cm long is cut into two pieces. One piece is bent into a square, while the other is bent into a rectangle that is twice as long as it is wide. Determine the side length x of the square that minimizes the total area enclosed by the two pieces of wire (see figure). Fully justify your answers! 50 cm 50 cm 2w 2w14 (15) Consider the following function and its derivatives: -12 f(I) = ( 1+2)(1- 2) f'(x) = 8x -8(3.2 + 4) (2+2)2(1- 2)2 f" (2) = 7 (+2) 3(1 - 2)3 [7pts] Give the final answer for each part below in the answer box. Show the rest of your work in the space provided. (a) Give the equations of all horizontal and vertical asymptotes. (If there are none, write "none".) Justify your answers by evaluating the appropriate limits below. Horizontal asymptotes: Vertical asymptotes: Show your work (evaluate the appropriate limits):(14) Determine each of the following limits. You may use any method we have covered in this [4pts] course. Show your work! (a) lim sin(t) t-+0 sin(2t) lim Sinct ) sin (24) t -0 Sin 2' lim (e37 + 1)