NO CALCULATORS: 1. Find A) 1 B) 0 C) D) 2. Find the points of discontinuity of the function y of discontinuity.

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1 AP CALCULUS BC NO CALCULATORS: MIDTERM REVIEW 1. Find lim 7x 6x x 7 x 9. 1 B) 0 C) D). Find the points of discontinuity of the function y of discontinuity. x 9x 0. For each discontinuity identify the type x 5 A. Removable discontinuity at x 7 B. Removable discontinuity at x 5 Removable discontinuity at x 7 Infinite discontinuity at x 5 C. Removable discontinuity at x 5 D. Oscillating discontinuity at x 5 Infinite discontinuity at x 7 Removable discontinuity at x 5 1. Find y if y x 7x x x 1. 1 B) y x x C) y x x D) y x x y x x 8 1. Suppose u and v are differentiable at x 6, and that u(6) 5, v(6), u(6) 8, and v(6) 9. d u Find ( ) at x 6. v 9 B) 61 C) D) Find if 8 y (x 5). (x 5) 7 B) 8 (x 5) C) 7 8(x 5) D) 7 x (x 5) 6. Find if 1 y tan ( x) x B) 1 9x C) x D) 1 9x 1 9x 7. Find if 5 y x. 15ln() B) 5x ln() C) 5x 5 ln() D) 5x 15 ln()

2 8. If f( x) x x 9, 6, then, according to the Mean Value Theorem, there is at least one point c in, 6 at which. is continuous on, 6 and differentiable on f() c 6 B) f() c 6 C) f() c 5 D) f() c 5 9. Find the function whose derivative is f ( x) 6x and whose graph passes through the point P(0, 1). f( x) 6 B) f ( x) x x C) f( x) 6x 1 D) f x x x ( ) Find the linearization L( x) of f( x) x 5x 17 at x. L( x) x B) Lx ( ) x 5 C) Lx ( ) x 17 D) Lx ( ) x Express n lim (ck ck 7) xk P 0 k 1 as a definite integral on the interval,6. 6 (1 6 7) x x B) 6 ( 7) x x C) 6 (1x 6 ) x D) ( 7) 6 x x 1. Use the Fundamental Theorem of Calculus with the chain rule to find x if y (7 7 t) dt. 6x B) 1 6x C) 1 1x D) 7 7 x 1. Evaluate the integral x ln x ln B) 0 7 ln C) 81 ln 9 D) 81 ln 5 1. Which of the following integrals gives the length of the curve y cos x from x 0 to x 5? 5 1 cosx B) cos x C) sin x D) sinx 15. Evaluate the integral secttantdt. sec t C B) sect C C) sect C D) tan t C 16. Let. What is the value of a if f has a local minimum at 6 f ( x) x ax x? a 7 B) a 0 C) a 16 D) a 7

3 17. Evaluate the integral ln( x) x ln xx C B) 1 C x C) 1 C D) ln x x x x C 18. For which of the following differential equations will a slope field show nothing but negative slopes in the fourth quadrant? x B) xy 5 y C) y D) x xy 19. (calculator OK on this one) Use Euler s Method with x 0.1, x y and y 0 when x 1 to find the value of y when x B) 0. C) 0. D) Find y if xy and y 1 when x 0 x y B) x e C) x y D) xy 1 dp 1. (calculator OK on this one) The logistic differential equation 0.0 P(90 P) describes the dt growth of a population P, where t is measured in years. Find the rate at which the population is growing when it is growing the fastest. 81 B) 90 C) 5 D).0 CALCULATORS OK:. A tanker is spilling oil into the water resulting in an oil slick that is close to circular. At the time that the slick s diameter is growing at the rate of 7m/sec, the diameter is 00 meters. At what rate is the area of the oil slick increasing? m /sec B) 98.0 m /sec C) m /sec D) m /sec. Use LRAM to compute the area under the curve described by y x 9 over the interval 0 x. 15 B) 1.5 C).5 D) Find the average value of the function 1over the interval,6. y x x 1.67 B) 6.67 C) D) The function vt () 16t 5tis the velocity in m/sec of a particle moving along the x-axis, where t is measured in seconds. Use analytic methods to find the particle s displacement for 0 t 7. Round your answer to the nearest 1 m. 5 m B) 1707 m C) 19 m D) 66 m

4 6. Let f( x) x x 5x 0 and let g be the inverse function of f. What is the value of g (0)? 1 B) C) 1 5 D) 5 7. Find the area of the region enclosed by 500 B) 50 y x y 5. C) 1000 D) 1000 x 5 and 8. A cup of coffee with temperature 10 F is placed in a freezer with temperature 0 F. After 6 minutes, the temperature of the coffee is 6. F. When will its temperature be 0F? Round your answer to the nearest minute. 1 minutes after being placed in the freezer B) minutes after being placed in the freezer C) 0 minutes after being placed in the freezer D) 1 minutes after being placed in the freezer 9. The solid lies between planes perpendicular to the x-axis at x and x. The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle y x to the semicircle y x. Find the volume of the solid. 6 B) 18 C) D) 88

5 OPEN ENDED REVIEW: x 1. Let f be the function defined by f( x) ( x +1) e for x. a) For what value of x does f reach its absolute maximum. Justify your answer. b) Find the x-coordinates of all points of inflection of f. Justify your answer. c) Sketch the graph.. A particle moves along the x-axis with an acceleration given by at () cos tfor t 0. At t 0, the velocity, vt (), of the particle is and the position x() t is 5. a) Write an expression for the velocity, vt () of the particle. b) Write an expression for the position x() t. c) For what values of t is the particle moving right? Justify your answer. d) Find the total distance traveled by the particle from t 0 to t.. Let R be the region enclosed by the graphs of y x e, y x, and the lines x 0 and x. a) Find the area of region R. b) Find the volume of the solid generated when R is revolved about the x-axis. c) Set up an integral expression in terms of a single variable for the volume of the solid generated when R is revolved about the y-axis and then find the volume.

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