Calc Multiple Choice Answers

The graph of a function f is shown above. Which of the following statements about f is false? : f is continuous at x=a

Let f be the function given f(x)=3e^(2x) and let g be the function given by g(x)=6x^3. At what value of x do the graphs of f and g have parallel tangent lines? : -0.391

If f is a continuous function and if F'(x)=f(x) for all real numbers x, then the integral [1,3] f(2x)dx= : (1/2)F(6)-(1/2)F(2)

If a cannot = 0, then the limit, as x approaches a, [(x^2-a^2)/(x^4-a^4)] is : 1/(2a^2)

Let F(x) be an antiderivative of [(lnx)^3]/x. If F(1)=0, then F(9)= : 5.827

If g is a differentiable function such that g(x)<0 for all real numbers x and if f'(x)=(x^2-4)g(x), which of the following is true? : f has a relative minimum at x=-2 and a relative maximum at x=2.

The graph of f is shown in the figure above. If the integral on [1,3] f(x)dx=2.3 and F'(x)=f(x), then F(3)-F(0)= : 4.3

The graph of the function y=x^3+6x^2+7x-2cosx changes concavity at x= : -1.89

What is the area of the region in the first quadrant enclosed by the graphs of y=cosx, y=x, and the y-axis? : 0.400

The base of a solid S is the region enclosed by the graph of y=sqrt(lnx), the line x=e, and the x-axis. If the cross sections of S perpendicular to the x-axis are squares, then the volume S is : 1

Which of the following are antiderivatives of f(x)=sinxcosx? : I and III only

If y=(x^3=1)62, then dy/dx= : 6x^2(x^3=1)

The graph of f', the derivative of the function f, is shown above. Which of the following statements is true about f? : f is increasing for -2<=x<=0.

The integral of (x^2)(cos(x^3))dx= : (1/3)sin(x^3) + C

The graph of a function f is shown above. At which value of x is f continuous, but not differentiable? : A

If y=(x^2)sin(2x), then dy/dt= : 2x(sin2x + xcos2x)

A curve has slope 2x + 3at each point (x,y) on the curve. Which of the following is an equation for this curve if it passes through the point (1,2)? : y=x^2+3x-2

Let f be the function given above. Which of the following statements are true about f ? : I and II only

A particle moves along the x-axis so that at time t>=0 its position is given by x(t)=2t^3-21t^2+72t-53. At what time t is the particle at rest? : t=3 and t=4

What is the slope of the tangent to the curve 3y^2 -2x^2=6-2xy at the point (3,2)? : 4/9

If f(x)=(x-1)(x^2+2)63, then f'(x)= : (x^2 +2)^2(7x^2-6x+2)

The integral [sin(2x)+cos(2x)]dx= : -1/2cos(2x)+(1/2)sin(2x)+C

The graph of the piecewise linear function f is shown in the figure above. If g(x)= on [-2,x] the integral f(t)dt, which of the following values is greatest? : g(1)

The graph of the function f is shown above for 0 ≤ x ≤ 3. Of the following, which has the least value? : Right Riemann sum approximation of the integral on [1,3] of f(x)dx with 4 subintervals of equal length

The integral of x/(x^2-4)= : (1/2)ln(x^2-4) + C

The graph of the function f shown above has horizontal tangents at x= 2 and x = 5. Let g be the function defined by g(x)= on [0,x] the integral f(t)dt. For what values of x does the graph of g have a point of inflection? : 2 and 5 only

23. A rumor spreads among a population of N people at a rate proportional to the product of the number of people who have heard the rumor and the number of people who have not heard the rumor. If p denotes the number of people who have hear the rumor, which of the following differential equations could be used to model this situation with respect to time t, where k is a positive constant? : dp/dt=kp(N-p)

24. Which of the following is the solution to the differential equation dy/dx+(x^2)/y with the initial condition y(3)=-2 ? : y=-sqrt[(2x^3)/3 - 14]

Let f be a differentiable function such that f(3) = 15, f(6) = 3, f ′(3) = -8, f ′(6) = -2. The function g is differentiable and g(x) = f -1(x) for all x. What is the value of g′(3)? : -1/2