SE 1
The graph of y=3x^2-x^3 has a relative maximum at ?
(2,4) only (C)
The integral of sin(3x+4)dx=?
-1/3cos(3x+4)dx (A)
Suppose that f(x) is an even function and let the integral from 0,1 f(x) dx = 5 and the integral from 0,7 f(x) dx=1. What is the integral from -1,-7 f(x)dx?
-4 (B)
If F(x) = (x^2+9)/(x+3) is continuous at x=-3, then f(-3)=?
-6 (E)
The figure at the right shows a road running in the shape of a parabola at the bottom of a hill at A to point B. At B it changes to a line and continues at C. The equation for the road is.... B is 1000 feet horizontally from A and 100 feet higher. Since the road is smooth, R'(x) is continuous. What is the value of B?
.2 (A)
Lim as x approaches infinity of 10^8x^5.../10^9x^6...
0 (A)
The average value of the function f(x) = cos (1/2x) on the closed interval [0,4] is?
1/2sin(2) (E)
Suppose f(x) = ln (3x) and f^-1(x) denotes the inverse of f. Then the integral of f^-1(x) dx=?
1/3e^x+c (B)
Let f be differentiable for all x. The graph of f'(x) is shown below. If f(2)=10, which of the following best approximates the maximum value of f(x)?
110 (E)
The amount A(t) of a certain item produced in a factory is given by A(t) = 4000+48(t-3)-4(t-3)^3 where t is in hours since the beginning of the workday at 8am. At what time is the production increasing most rapidly?
11am. (C)
Let f and g be differentiable functions such that f(1)=4, g(1)=3, f'(3)=-5,f'(1)=-4,g'(1)=-3 and g'(3)=2. If h(x)=f(g(x)), then h'(1)=?
15 (B)
If F(x)=e^sinx, how many zeros does f'(x) have on the closed interval [0,2pi]?
2 (B)
If the graph of f(x)=2x^2+k/x has a point of inflection at x=/1, then the value of k is ?
2 (c)
Let f(x) be the function defined by f(x)={x, x_<0, x+1, x>0. The value of the integral from -2,1 x f(x) dx =?
7/2 (C)
A population grows according to the equation P(t)=6000-5500e^-.159t for t_>0. This population will approach a limiting value as time goes on. During which year will the population reach half of this limiting value?
Fourth (C)
If f and g are differentiable functions, then the integral from 0,g(x) f'(t)dt =?
f(g(x))-f(0) (D)
For which pair of functions f(x) and g(x) below will the limit as x approaches infinity of f(x)/g(x)=0?
f(x), ln x and g(x), e^x (C)
At how many points on the curve y=4x^5-3x^4+15x^2+6 will the line tangent to the curve pass through the origin?
one (A)
Let R(t) represent the rate at which water is leaking out of a tank, where t is measured in hours. Which of the following represents the total amount of water that leaks out in the first three hours?
the integral from 0,3 R(t)dt. (C)
For what values of x is the graph of y=2/4-4 concave downward?
x>4, E
The integral from 0,3 x/x+1 dx =?
3-2ln2 (C)
If x>0, the integral of x^-1/3 is ?
3/2x^2/3+c (D)
The values of a function are given in the table to the right. The Trapezoidal Rule approximation for the integral from 0,10 f(x) dx is? (This one is brute memorization, I'm not writing out the table) (0,20), (1,19.5)(2,18),(3,15.5),(4,12),(5,7.5)...
32.500 (B)
A particle moves along the x-axis in such a way that its position at time t is given by x(t)= (1-t)/(1+t). What is the acceleration of the particle at time t=0?
4 (C)
The maximum value of f(x)=2x^3-9x^2+12x-1 on [-1,2] is?
4 (E)
The integral of 1/sqrrt of 4-x^2 dx =
arcsin(x/20+c (A)
