minutes/question 26 minutes

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1 st Set Section I (Multiple Choice) Part A (No Graphing Calculator) 3 minutes/question 6 minutes. What is 3 3 cos cos lim? h hh (D) - The limit does not exist.. At which of the five points on the graph in the figure on the right are dy d y and dx dx both negative? A B C (D) D E 3. A city is built around a circular lake that has a radius of mile. The population density of the city is f(r) people per square mile, where r is the distance from the center of the lake, in miles. Which of the following expressions gives the number of people who live within mile of the lake? r f r dr ( ) ( ) ( ) r f r dr (D) ( ) r f r dr r f r dr r f ( r) dr 4. 3 The position of a particle moving along a line is given by s( t) t 4t 9t 7 for t. For what values of t is the speed of the particle increasing? 3 < t < 4 only t > 4 only t > 5 only (D) < t < 3 and t > 5 3 < t < 4 and t > 5

2 5. x x dx 3 x x C x x C 3 x x C 3 (D) 5 3 x x C x x x C 6. What is x 4 lim x x 4 x? 4 (D) The limit does not exist. 7. The figure on the right shows the graph of y 5x x and the graph of the line y x. What is the area of the shaded region? (D) If F is a continuous function for all real x, then F () Fa ( ) (D) F () F ( a) ah lim F ( x) dx h h is a

3 9. The function f, whose graph consists of two line segments, is shown on the right. Which of the following are true for f on the open interval (a, b)? I. The domain of the derivative of f is the open interval (a, b). II. f is continuous on the open interval (a, b). III. The derivative of f is positive on the open interval (a, c). I only III only I, II, and III II only (D) II and III only Questions and refer to the following graph and information. A bug is crawling along a straight wire. The velocity, v(t), of the bug at time t, t, is given in the graph above.. According to the graph above, at what time t does the bug change direction? 5 6 (D) 8. According to the graph above, at what time t is the speed of the bug greatest? 5 6 (D) 8

4 . The line perpendicular to the tangent of the curve represented by the equation y x 6x 4 at the point (, 4) also intersects the curve at (D) 3 3. Let f be a function whose domain is the open interval (, 5). The figure on the right shows the graph of f. Which of the following describes the relative extrema of f and the points of inflection of the graph of f? relative maximum, relative minimum, and no point of inflection. relative maximum, relative minima, and no point of inflection. relative maximum, relative minimum, and point of inflection. (D) relative maximum and points of inflection. relative minimum and points of inflection.

5 st Set Section I (Multiple Choice) Part B (Graphing Calculator Permitted) 4 minutes/question 4 minutes 4. The graph of a function f is shown on the right. x b If lim f ( ) exists and f is not continuous at b, then b = - (D) 3 5. x f( x ) Let f be a function such that f ( x) for all x in the closed interval shown in the table above. Which of the following must be true about f (.)? f (.) f (.).6.6 f (.).8 (D).8 f (.). f (.).,. Selected values of f are 6. The graph of the function f shown on the right consists of two line segments. If g is the function defined by then g(-) = - - (D) g( x) f ( t) dt, x

6 7. The graphs of five functions are shown below. Which function has a nonzero average value over the closed interval,? (D) 8. The graph of the function f on the right consists of four semicircles. If g( x) f ( t) dt, where is gx ( ) nonnegative? 3, 3 x 3,,, 3 only (D) 3,, 3 only only, only 9. If f is differentiable at x = a, which of the following could be false? f is continuous at x = a. lim ( ) xa exists. f ( x) f ( a) lim x a x a exists. (D) f ( a) is defined. f ( a) is defined.

7 . Three graphs labeled I, II, and III are shown on the right. One is the graph of f, one is the graph of f, and one is the graph of f. Which of the following correctly identifies each of the three graphs? f f f I II III I III II II I III (D) II III I III II I. A particle moves along the x-axis so that at any time t its velocity is given by v( t) ln( t ) t. The total distance traveled by the particle from t = to t = is (D) t t. Let g be the function given by gt ( ) sin cos 6. For t 8, g is decreasing most rapidly when t = (D) If the function g is defined by then g has a local minimum at x = x ( ) sin( ) (D).7.57 gx t dt on the closed interval x 3,

8 4. If f is continuous for all x, which of the following integrals necessarily have the same value? b I. f ( x ) dx ba bc II. f ( x a ) dx a III. f ( x c ) dx ac I and II only II and III only No two necessarily have the same value. I and III only (D) I, II, and III 5. A solid has a rectangular base that lies in the first quadrant and is bounded by the x and y-axes and the lines x = and y =. The height of the solid above point (x, y) is + 3x. Which of the following is a Riemann sum approximation for the volume of the solid? n 3i i n n 3 n i i i n n (D) n i i 6i n n n 3i i n n n i 6i n n 3 6. If the function f is defined by f ( x) x and g is an antiderivative of f such that g(3) = 5, then g() = (D) Let f be defined as follows, where a. f( x) x a x a,, for x a for x a Which of the following are true about f? I. lim f ( x ) exists. xa II. f( a ) exists. III. f( x ) is continuous at x = a. None II only I, II, and III I only (D) I and II only

9 st Set Section I (Multiple Choice) Part A (No Graphing Calculator). A 6. B. E. B 7. B. B 3. D 8. E 3. E 4. E 9. D 5. D. D Section I (Multiple Choice) Part B (Graphing Calculator Permitted) 4. B 9. E 4. A 5. D. E 5. D 6. B. C 6. B 7. E. B 7. D 8. A 3. E