Show your work. 1. e 2x+l 1 Evaluate: 1%} x _ s1n2 (3x) 2. Evaluate: Inn 2 x>0 x x2 9 . . if x i 3 . . 3. Find the value of c where f (x) = x _ 3 is continuous atx = 3. C if x = 3 . . . . . 3 2x 4. Determlne the pomts of d1scont1nu1ty of f (x) = + x2 x+4 5. Find y", ify = x6 + +x2-2x+5 6. If ff f(x)dx = 3 and f15f(x)dx = 4, then f: 3 f(x)dx = 7. Find the area determined by the two curves f (x) = 4x and g(x) = x2 8. Findy = f(x) if f"(x) = x2, f'(0) =4 and f(0) = 3. 9. If a ball is thrown into the air with a velocity of 20 ft. /s, its height (in feet) after t seconds is given by S(t) = 201 8:2 . Find the velocity when t = 10. A circular plate is heated in an oven. Its radius increases at the rate of 0.2 cm/min. At what rate is the plate's area increasing when the radius is 5 cm? Hint: Use A = zrr2 11. Let f (x) = x2 4x on [0, 4-]. Find the value(s) of c in (0, 4-) guaranteed by Rolle's Theorem . 12. Let y =f(x) be a differentiable function for which the graph of its derivative, f ', is given below: On what interval(s) is the graph off a) increasing? b) concave up 9x x2+9' 13. Determine which of the following is not true for the graph of f (x) = a) f is continuous on (00, 00). b) f has no vertical asymptote. c) f has a horizontal asymptote: y = 0. d) f has no point of inection. e) f has a relative maximum and a relative minimum. 14. Find the differential dy if y = (33:2 +1)5 . . . d x 15. F 1nd the derivative E U1 (In cost) dt]