2012 Calc BC No Calc
22. The function f has a continuous derivative. The table above gives values of f and its derivative for x=0 and x=4. If int[0,4] f(x)dx = 8, what is the value of int[0,4] xf'(x)dx?
A) -20
9. The function f is twice differentiable, and the graph of f has no points of inflection. If f(6) = 3, f'(6) = -1/2, and f''(6) = -2, which of the following could be the value of f(7)?
A) 2
28. The function f is given by f(x) = sin((x+1)/x^2). Which of the following statements are true?
A) I only
13. For time t>0, the position of a particle moving in the xy-plane is given by the parametric equations x=4t+t^2 and y=1/(3t+1). What is the acceleration vector of the particle at time t=1?
B) (2,9/32)
7. let y=f(x) be the solution to the differential equation dy/dx = x-y-1 with the initial condition f(1)=-2. What is the approximation for f(1.4) if Euler's method is used, starting at x=1 with two steps of equal size?
B) -1.24
23. What is the slope of the line tangent to the polar curve r=2(theta) at the point theta = pi/2?
B) -2/pi
18. If f(x) = arccos(x^2), then f'(x) =
B) -2x/(sqrt(1-x^4))
11. The sides and diagonal of the rectangle above are strictly increasing with time. At the instant when x=4 and y=3, dx/dt=dz/dt and dy/dt=kdz/dt. What is the value of k at that instant?
B) 1/3
6. int (e^x/(1+e^x))dx
B) ln(1+e^x) + C
14. int (8/(x^2-4)) dx =
C) 2ln|(x-2)/(x+2)| + C
2. A particle moves along the x-axis so that any time t>_ 0, its velocity is given by v(t) = sin(2t). If the position of the particle at time t=pi/2 is x=4, what is the particle's position at time t=0?
C) 3
26. The coefficients of the power series sum[n=0,inf] a_n(x-2)^n satisfy a_0 =5 and a_n = ((2n+1)/(3n-1))*a_(n-1) for all n>_ 1. The radius of convergence of the series is
C) 3/2
3. What is the value of sum[n=0,inf] (-2/3)^n
C) 3/5
10. A function f has Maclaurin series given by 1 + x^2/2! +x^4/4! +x^6/6! +...+ x^2n/(2n)! +.... Which of the following is an expression for f(x)?
D) 1/2(e^x+e^-x)
8. The function f is continuous on the closed interval [0,6] and has the values given in the table above. The trapezoidal approximation for int[0,6] f(x)dx found with 3 subintervals of equal length is 52. What is the value of k?
D) 10
1. If f(x) = (3x-2)/(2x+3), then f'(x) =
D) 13/(2x+3)^2
24. The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant?
D) 2
19. What is the slope of the line tangent to the curve y+2 = x^2/2 -2sin(y) at the point (2,0)?
D) 2/3
17. The radius of convergence for the power series sum[n=1,inf] (x-3)^2n/n is equal to 1. What is the interval of convergence?
D) 2<x<4
12. If f'(x) = 2/x and f(sqrt(e)) = 5, then f(e) =
D) 6
5. The length of the curve y=x^4 from x=1 to x=5 is given by
D) int[1,5] sqrt(1+16x^6) dx
16. If f'(x) = |x-2|, which of the following could be the graph of y=f(x)?
E)
21. The function f given by f(x) = 9x^2/3 +3x -6 has a relative minimum at x=
E) 0
27. If f is the function given by f(x) = int[4,2x] (sqrt(t^2-t))dt, then f'(2) =
E) 2sqrt(12)
20. Which of the following series converge?
E) II and III only
25. The table above shows several Riemann sum approximations to int[0,1] (1/x) dx using right hand endpoints of n subintervals of equal length of the interval [0,1]. Which of the following statements best describes the imit of the Riemann sums as n approaches infinity?
E) The limit of the Riemann sums does not exist because int[0,1] (1/x) does not exist.
4. For values of h very close to 0, which of the following functions best approximates f(x) = (tan(x+h)-tan(x))/h?
E) sec^2(x)
15. The slope field for a certain differential equation is shown above. Which of the following could be a solution to the differential equation with the initial condition y(0) = 1?
E) y=1/(1+x^2)
