Let f(x) = x3 + x 1 and 30:) = x3 x2 + 2x + 1. Find the area A of the bounded region between the graphs offand g. (10 pts) Consider the graph of the...

10. 11. 12. Let f(x) = x3 + x — 1 and 30:) = x3 — x2 + 2x + 1. Find the area A of thebounded region between the graphs offand g. (10 pts) Consider the graph of the curve with parametric equations x(t) = —3 sin(2t),y(t) = 4cos(2t), for t 2 0. a. Sketch the graph of the curve, and indicate the direction of increasing t. (Lookingahead to part c might be helpful.) (5 pts) b. Find the slope of the line tangent to the graph of this curve when t = E. No approximations. Find 2—: n by using the formula in the box of section 2.2, p. 169.t:—6(5 NS)2 2c. Show that x? + {—6 = 1. A curve with this equation is called an (fill in theblank). (5 pts) d. By using implicit differentiation on the equation in part c), find 2—: in terms ofxand y. Calculate x (E) and y (E), and reconcile your answer to part b). (5 pts) Consider the function f(x) = i lnx'a. Determine the domain off. (5 pts)b. Find the vertical asymptote(s), if any, of this function. Use limits to justify thatyou have in fact found the asymptote(s). (5 pts) c. Find the horizontal asymptote(s), if any, of this function. Use limits to justify thatyou have in fact found the asymptotes. (5 pts)