Packet 1 Ap calc

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

D) 1/4 - e^-4/4 : Integration from 0 to 4 of e^-4x dx=

B) f is increasing for -2<x<0 : The graph of f1, the derivative of the function f, is shown above. which of the following statements is true about f?

B) 1/3sin(x^3)+C : integration of x^2cos(x^3) dx

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

E) 2x(sin 2x+x cos 2x) : If y=x^2sin2x, then dy/dx=

D) y=x^2+ 3x-2 : A curve has slope 2x+3 at 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)

D) I and II only : f(x)= x+2 if x<3 =4x-7 if x>3Let f be the function given above. whih of the followng statements is true about f?

E) t=3 and t=4 : 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

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

C) 4pi m^2/sec : 78) The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumerence of teh circle is 20pi meters?

D) I and II only : 79) For which of the following does lim x approaching 4 f(x) exist?

A) 112F : 84) A pizza heated to temp of 350 degrees F, is taken out of an oven and placed in a 75F room at time t=0 minutes. The temp of the pizza is changing at a rate of -110e^-0.04t degrees F per minute. To the nearest degree, what is the temp of the pizza at time t=5

A : 85) If a trapezoidal sum overapproximates integration from 0 to 4 f(x) dx, and a right Riemann sum underapproximtes it, which of the following could be the graph of y=f(x)

B : 90) For all x in the closed interval (2,%), the function f has a positive first derivative and a negative second derivative. which of the following could be a table of values for f?

E) 3.346 : 91) a particle moves along the x-axis so that at any time t>0, its acceleration is given by a(t)= ln(1+2^t). If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is