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. Find lim B) C) D). Find the points of discontinuit of the function of discontinuit. 9. For each discontinuit identif the tpe A. Removable discontinuit at 7 B. Removable discontinuit at Removable discontinuit at 7 Infinite discontinuit at C. Removable discontinuit at D. Oscillating discontinuit at Infinite discontinuit at 7 Removable discontinuit at. Find if 7. B) C) 8 D) 8. Suppose u and v are differentiable at, and that u(), v(), u() 8, and v() 9. d u Find ( ) at. v 9 B) C) D) 9 9. Find if 8 (. ( 7 B) 8 ( C) 7 8( D) 7 (. Find if tan ( ). 9 B) 9 C) D) Find if. ln() B) ln() C) ln() D) ln()

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

3 7. Evaluate the integral ln( ) ln C B) C C) C D) ln C 8. For which of the following differential equations will a slope field show nothing but negative slopes in the fourth quadrant? B) C) D) 9. (calculator OK on this one) Use Euler s Method with., and when to find the value of when... B). C). D).8. Find if and when B) e C) D) dp. (calculator OK on this one) The logistic differential equation. P(9 P) describes the dt growth of a population P, where t is measured in ears. Find the rate at which the population is growing when it is growing the fastest. 8 B) 9 C) D). 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 meters. At what rate is the area of the oil slick increasing? 7. m /sec B) 98. m /sec C).9 m /sec D) 99. m /sec. Use LRAM to compute the area under the curve described b 9 over the interval. B). C). D) 7.. Find the average value of the function over the interval,..7 B).7 C).7 D).7. The function vt () t tis the velocit in m/sec of a particle moving along the -ais, where t is measured in seconds. Use analtic methods to find the particle s displacement for t 7. Round our answer to the nearest m. m B) 77 m C) 9 m D) m

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

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