AP Calculus AB/BC ilearnmath.net 21. Find the solution(s) to the equation log x =0.

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1 . Find the solution(s) to the equation log =. (a) (b) (c) (d) (e) no real solutions. Evaluate ln( 3 e). (a) can t be evaluated (b) 3 e (c) e (d) 3 (e) 3 3. Find the solution(s) to the equation ln( +)=3. (a) (b) 3 ln (c) e 3 ln (d) e 3 (e) 4. Which of the graphs shown below best represents the graph of y = log? (a) Graph (b) Graph (c) Graph 3 (d) Graph 4 (e) Graph 5 Graph Graph Graph 3 Graph 4 Graph 5. Find lim. PART B (a) (b) 3 (c) (d) (e) doesn t eist 3. Find lim (a) 3 4 (b) 4 (c) (d) (e) +

2 3. Find lim e. (a) (b) e (c) (d) + (e) 4. The graph of a function g() is shown below. Which of the following statements are true of g()? I. lim g() = III. lim g() does not eist V. lim g() does not eist II. lim g() = IV. lim g() = (a) only I and IV are true (b) only I and V are true (c) only II and IV are true (d) only II and V are true (e) only III and V are true 5. f () can be defined as: (a) lim Δ (d) lim Δ f( +Δ) f() f( +Δ) f() Δ (b) lim f( +Δ) f() Δ (c) lim Δ f( +Δ) f() Δ 6. Consider again the function g() whose graph is shown in problem 4. Which of the following statements are true of g()? I. g is continuous at = II. g is continuous at = III. g is differentiable at = IV. g is differentiable at = V. g is differentiable at = (a) only I and IV are true (b) only II and IV are true (c) only I and V are true (d) only II and V are true (e) only III and V are true 7. The graph of a function f() is shown below. At which of the following points is the value of the derivative f () biggest? (a) at = (b) at = (c) at =3.5 (d) at =6 (e) at =7 8. Consider again the function f() whose graph is shown in problem 7. At which points is the second derivative f () negative? (a) at = and =3.5 (b) at =, = and =3.5 (c) at = 6 only (d) at = 7 only (e) at = 6 and =7

3 9. Let f() =ln cos. Find f (). (a) (d) cos ( sin ) (b) ( sin ) (c) cos ln sin ( cos sin ) cos. Let y =4e tan. Find dy d. (a) 4e tan sec (b) 4e tan (d) 4e tan cot. Let f() =sin. Find f (). (e) 4 sec + (c) 4e tan (a) π (b) (c) (d). The equation of the line tangent to the graph of f() = +5 at the point with -coordinate = is: (a) y =9 4 (b) y =9 (c) y =9 4 (d) y = Let f() = 3 3. Which of the following statements are true? I. f() has local maima at both = and =. II. f() has a local minimum at = and an inflection point at =. III. f() has both a local minimum and an inflection point at =. (a) only I is true (b) only II is true (c) only III is true (d) only I and III are true (e) none of the statements is true 4. A commercial nursery has yards of fencing which the owners plan to use to enclose as large a rectangular garden as possible. The garden will be bounded on one side by a barn, so no fencing is needed on that side. How large will the garden be (in square yards)? (a) 5, sq yds (b) 5, sq yds (c),88.89 sq yds (d) 6,5 sq yds 5. The width of a rectangle is increasing at a rate of cm/sec, and its length is increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing when its width is 4 cm and its length is 5 cm? (a) 3 cm /sec (b) 3 cm /sec (c) 5 cm /sec (d) cm /sec

4 6. A rock is dropped from a height of 4 feet and falls toward the earth in a straight line; t seconds after it is dropped, it has fallen a distance of s(t) =6t feet. At what speed is the rock traveling when it hits the ground? (a) ft/sec (b) 3 ft/sec (c) 64 ft/sec (d) 3 ft/sec (e) 6 ft/sec PART C. Which of the following gives the area between the curves y = and y = over the interval [, ]? (a) (d) ( ) d (b) ( ) d (c) ( ) d ( ) d + ( ) d. Suppose that f() is a continuous function with the following properties: f () =cos, f (π) = and f() = 4. What is f(π)? (a) (b) π (c) π + (d) 6 + π (e) 3. Suppose that the function f() is defined by f() = e t t dt. Find f (). (a) e ln (d) e e (b) e ln e (c) e (e) the integral can t be computed, so it s impossible to give the answer 4. Let F () = statements are true? f(t) dt, where f(t) is the function shown below. Which of the following I. F ( ) >F( 4) II. F () >F() III. F () > IV. F ( ) = t (a) only I is true (b) only II is true (c) only III is true (d) only I and II are true (e) only II and IV are true

5 5. Suppose that f() = AP Calculus AB/BC ilearnmath.net +. Find f () d. (a) (b) 8 5 (d) (c) Which of the following statements about indefinite integrals are true? I. f()+g() d = f() d + g() d II. f()g() d = f() d g() d III. f (g())g () d = f(g()) + C IV. [f()] n d = [f()]n+ + C n + (a) only I and II are true (b) only I and III are true (c) only I and IV are true (d) only I, II and IV are true (e) only I, III and IV are true 7. Find the volume of the solid obtained by rotating the region bounded by y = and y = over the interval [, ] around the -ais. (a) (d) π( 4 ) d (b) π( y y) dy (e) π( ) d π(y y ) dy (c) π( 4 ) d 8. The integral ln d can be found by (a) making the substitution u = ln (b) making the substitution u = (c) using integration by parts, with u =ln and dv = (d) taking the reciprocal of ln d 9. The integral sin d can be found by. Find (a) making the substitution u = (b) making the substitution u = sin (c) using integration by parts, with u = sin and dv = d (d) using integration by parts, with u = and dv = sin d ln 3 e d +e (a) ln (b) (c) π (d) π 4 (e)

6 . Find lim sin 3. AP Calculus AB/BC ilearnmath.net (a) (b) (c) 6 (d) (e) does not eist 3. Find d. (a) (b) (c) (d) (e) the integral diverges 3. Which of the following improper integrals converge to a finite value? (I) e d (II) 3 d (III) + d (a) I only (b) III only (c) I and II only (d) I and III only (e) all of them 4. The second order Taylor polynomial at = for f() =e is (a) (d) + (b) + (e) + (c) Which of the following series converge? (I) n= n (II) n= n (III) n= n n (a) (I) only (b) (III) only (c) (I) and (II) only (d) (I) and (III) only (e) all of them 6. The radius of convergence of the power series n is n= (a) (b) (c) (d) 3 (e)