Work on the following;

7. (12 points) (a) Find / (3cos(x) + 2) do (b) A function f(x) satisfies f(2) = 3 and f'(2) = -6r' + 2r. Find the function f(z).6. (12 points) (a) Write, for n = 4, the left Riemann sum that approximates La 2r) dr. Sigma summation notation in your answer is preferred. (b) Evaluate (1 +2r) de using the fundamental theorem of integral calculus.10. (8 points) Water is pumped into a spherical balloon so the ballon's volume is increasing at a rate of 100cm /s. How fast is the radius of the balloon increasing when radius is 25cm? The volume V of a sphere is related to the radius r via V = Clearly show and explain your problem setup, steps, and work.2. (15 points) For each of the following, find dy Do not simplify. dr COST (a) y= 2r + 1 (b) y = (re)3 (c) my) + x] = 21. (6 points) Use the definition of derivative as a limit to find f'(a) for f(x) = r' -r and a = 1. Show your steps and your limit evaluations.3. (10 points) Find the following limits using analytical means (limit laws, I'llo toring, etc.) 3r - sinc (a) lim (b) lim E - 2x 3-Do 3r" + 5-3(x'+ 1) 9. (12 points) For the function f (r) = ; the derivative is f'(c) = (x3 - 1)' (a) Identify the horizontal and vertical asymptotes of f(I). (b) Identify intervals where f(x) is increasing and intervals where it is decreasing. (c) Identify the critical points and classify them as maxs, mins, or inflection points.5. (10 points) Let f(@) = 2r+c c