1. Simplify the expression sin(tan '(r)). 2. Does lim 1 4-5 2x + 10 exist? Explain your reasoning. 3. Determine lim VI - 9 I ko 20 -6 4. Show that there exists at least one solution to the equation e's = 3sin(r) on the interval [-4, 0). 5. Suppose that f(0) = 2, f(2) = 3, f(0) = -1, f(2) = 6, g(0) = 5, g(2) = 0, g (0) = 7 and #'(2) = 2. If y(I) = f(g(r)), determine y'(2). 6. Determine the derivative of f(r) = tan 7. Determine the equation of the tangent line to the implicitly-defined curve a y = y' - 6r at the point (2, -2). 8. Determine the slope of the tangent line to f(x) = p!"(?) at I = 2. 9. Determine the derivative of g(r) = (r + ear) sin() 10. Determine the equation of the tangent line to the implicitly-defined curve ray = y' - 6r at the point (2, -2). 11. Determine the equation of the tangent line to the implicitly-defined curve sin(r + y) = 4x -2y at the point (*, 2x). 12. Find the value of A such that the tangent line to f(r) = 2ed at (0, 2) is the same as the tangent line to the implicitly-defined curve (y - 3) = 2 - (x - 1) at the same point. 13. Find the global maximum and minimum for f (x) = = I 72 _ x + 1 on the interval [0, 3]. 14. Determine the local maximum and minimum and inflection points of the function f(r) = 12/5(6 -1)1/5. Show all your work. 15. Find the dimensions of a rectangle with area 1000 m' whose perimeter is as small as possible. 16. Suppose you start a company such that your profit is determined by P(r) = r(40-r) - (4r + 80). Determine the value of r to maximize your profit, if I is on the interval [0, 30]