Perform the following steps to find the maximum area of the rectangle shown in the figure. C: 3 A(x) = 2 et - 1 1 (a) Solve for c in the equation f(c) = f(c + x). lim c x-0+ 13x² et - 1 lim c- f\x)=13xe-* C+X e-1 (b) Use the result in part (a) to write the area A as a function of x. [Hint: A = xf(c)] Determine the required area. 4 L 5 6 (c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions of the rectangle of maximum area. (Round your answers to three decimal places.) x = 2.424 X f(c) = X (d) Use a graphing utility to graph the expression for c found in part (a). Use the graph to approximate lim cand lim c. X→ 00 Use this result to describe the changes in the dimensions and position of the rectangle for 0 < x < 0. As x → ∞, the width of the rectangle ---Select--- ✓, while the height of the rectangle ---Select--- ✓, and the rectangle moves --Select-- the ---Select---