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128 Cards in this Set

  • Front
  • Back
Which of the following defines a function f for which f(-x)=-f(x)?
--------------------------------------------
f(x) = x^2
f(x) = sin x
f(x) = cos x
f(x) = log x
f(x) = e^x
f(x) = sin x
ln(x-2) < 0
------------------
x < 3
0 < x < 3
2 < x <3
x > 2
x > 3
2 < x < 3
If f(x) = sqrt(2x + 5) - sqrt(x + 7)/ x - 2 for x =/ 2
f(2) = k
and if f is continuous at x = 2 then k =
-------------------------------------------------------
0
1/6
1/3
1
7/5
1/6
If 3x^2 + 2xy + y^2 = 2 then the value of dy/dx at x = 1 is
--------------------------------------------------
-2
0
2
4
not defined
not defined
What is lim 8(1/2 + h) ^8 - 8 (1/2) ^8/h
h -> 0
----------------------------------------
0
1/2
1
limit does not exist
can not be determined from the info given
1/2
For what value of k will x + k/x have a relative max at x = -2
-------------------------------------------
- 4
- 2
2
4
None of these
4
p(x) = (x + 2)(x + k) and if the remainder is 12 when p(x) is divided by x - 1, then k =
-------------------------------------------
2
3
6
11
13
3
When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is
------------------------------------
1/4 pi
1/4
1/pi
1
pi
1/pi
The point on the curve x^2 + 2y = 0 that is nearest the point (0, -1/2) occurs where y is
---------------------------------------
1/2
0
-1/2
-1
None of the above
0
If f(x) = 4/x-1 and g(x) = 2x, then the solution set of f(g(x)) = g(f(x)) is
-----------------------------------
{1/3}
{2}
{3}
{-1,2}
{1/3,2}
{1/3}
If the function f is defined f(x) = x^5 - 1, then f^-1, the inverse function of f, is defined by f^-1(x) =
----------------------------------------
1/^5sqrt(x)+1
1/^5sqrt(x+1)
^5sqrt(x-1)
^5sqrt(x)-1
^5sqrt(x+1)
^5sqrt(x+1)
If f'(x) and g'(x) exist and f'(x) > g'(x) for all real x, then the graph of y = f(x) and the graph of y = g(x)
------------------------------------
intersect exactly once
intersect no more than once
do not intersect
could intersect more than once
have a common tangent at each point of intersection
intersect no more than once
The graph of y = 5x^4 - x^5 has a point of inflection at
---------------------------------------
(0,0) only
(3,162) only
(4,256) only
(0,0) and (3,162)
(0,0) and (4,256)
(3,162)
If f(x) = 2 + | x - 3| for all x, then the value of the derivative f'(x) at x = 3 is
----------------------------------
-1
0
1
2
nonexistent
nonexistent
A point moves on the x-axis in such a way that its velocity at time t (t > 0) is given by v = lnt/t. At what value of t does v attain its max?
--------------------------------------
1
1/e^2
e
e^3/2
There is no max value for v
e
An equation for a tangent to the graph of y = arcsin x/2 at the origin is
-----------------------------------
x - 2y = 0
x - y = 0
x = 0
y = 0
pi x - 2y = 0
x - 2y = 0
At x = 0, which of the following is true of the function f defined by f(x) = x^2 + e^-2x?
------------------------------------------
f is increasing
f is decreasing
f is discontinuous
f has a relative min
f has a relative max
f is decreasing
d/dx (ln e^2x) =
-----------------------
1/e^2x
2/e^2x
2x
1
2
2
The area of the region bounded by the curve y = e^2x, the x-axis, the y-axis, and the line x = 2 is equal to
-------------------------------------------------------
(e^4/2)-e
(e^4/2)-1
(e^4/2)-(1/2)
2e^4 - e
2e^4 - 2
(e^4/2) - (1/2)
If sin x = e^y, 0 < x < pi, what is dy/dx in terms of x?
---------------------------------
- tan x
- cot x
cot x
tan x
csc x
cot x
A region in the plane is bounded by the graph of y = 1/x, the x-axis, the line x = m, and the line x = 2m, m>0. The area of this region
-------------------------------
is independent of m

increases as m increases

decreases as m increases

decreases as m increases when m < 1/2; increases as m increases when m>1/2

increases as m when m < 1/2; decreases as m increases when m > 1/2
is independent of m
If dy/dx = tan x, then y =
------------------------------------
1/2tan^2x + C
sec^2x + C
ln | sec x| + C
ln | cos x| + C
sec x tan x + C
ln | sec x| + C
The function defined by f(x) = sqrt(3) cos x + 3 sin x has an amplitude of
-----------------------------------
3-sqrt(3)
sqrt(3)
2sqrt(3)
3 + sqrt(3)
3sqrt(3)
2sqrt(3)
If a function f is continuous for all x and if f has a relative maximum at (-1,4) and a relative min at (3,-2), which of the following statements must be true?
-----------------------------------------
The graph f has a point of inflection somewhere between x= -1 and x= 3

f'(-1) = 0

The graph of f has a horizontal asymptote

The graph of f has a horizontal tan line at x = 3

The graph of f intersects both axes
The graph of f intersects both axes
If f'(x) = -f(x) and f(1) = 1, then f(x) =
----------------------------------------
(1/2)(e^-2x+2)
e^-x-1
e^1-x
e^-x
-e^x
e^1-x
If a,b,c,d and e are real numbers and a =/ 0 then the polynomial equation ax^7 + bx^5 + cx^3 + dx + e = 0 has
---------------------------------------------------
only one real root
at least one real root
an odd number of nonreal roots
no real roots
no positive real roots
at least one real root
What is the average (mean) value of 3t^3 - t^2 over the interval -1 <= t <= 2?
------------------------------------------
11/4
7/2
8
33/4
16
11/4
Which of the following is an equation of a curve that intersects at right angles every curve of the family y = 1/x + k (where k takes all real values)?
-----------------------
y = -x
y = -x^2
y = -1/3 x^3
y = 1/3 x^3
y = ln x
y = 1/3 x^3
At t = 0 a particle starts at rest and moves along a line in such a way that at time t its acceleration is 24t^2 feet per second per second. Through how many feet does the particle move during the first 2 seconds?
-------------------------------
32
48
64
96
192
32
The approximate value of y = sqrt(4 + sin x) at x = 0.12, obtained from the tangent to the graph at x = 0, is
------------------------------
2.00
2.03
2.06
2.12
2.24
2.03
Which is the best of the following polynomial approximations to cos 2x near x = 0?
-----------------------------
1+ x/2
1+x
1-x^2/2
1-2x^2
1-2x+x^2
1-2x^2
If y = tan u, u = v - 1/v, and v = ln x, what is the value of dy/dx at x = e?
------------------------
0
1/e
1
2/e
sec^2e
2/e
What are all values of k for which the graph of y = x^3 - 3x^2 + k will have three distinct x- intercepts?
---------------------------------
All k>0
All k<4
k = 0,4
0 < k < 4
All K
0 < k < 4
If d/dx(f(x)) = g(x) and d/dx(g(x)) = f(x^2), then d^2/dx^2(f(x^3)) =
-----------------------------
f(x^6)
g(x^3)
3x^2g(x^3)
9x^4f(x^6)+6xg(x^3)
f(x^6)+g(x^3)
9x^4 f (x^6) + 6x g(x^3)
the fundamental period of the function defined by
f(x) = 3 - 2cos^2 (pi x/3) is
---------------------------------------------------
1
2
3
5
6
3
If f(x) = x^3 + 3x^2 + 4x + 5 and g(x) = 5 then g(f(x)) =
-----------------------------
5x^2 + 15x + 25
5x^3 + 15x^2 + 20x + 25
1125
225
5
5
The slope of the line tangent to the graph of y = ln(x^2) at x = e^2 is
--------------------------
1/e^2
2/e^2
4/e^2
1/e^4
4/e^4
2/e^2
If f(x) = x + sin x, then f'(x) =
-------------------
1 + cosx
1 - cos x
cos x
sin x - cos x
sinx + x cos x
1 + cos x
If f(x) = e^x, which of the following lines is an asymptote to the graph of f?
-------------------------
y=0
x=0
y=x
y=-x
y=1
y=0
If f(x) = x - 1/ x + 1 for all x=/ 1, then f'(1)
-------------------------------
-1
-1/2
0
1/2
1
1/2
Which of the following equations has a graph that is symmetric with respect to the origin?
-----------------------------------
y = x + 1/x
y = -x^5 + 3x
y = x^4 - 2x^2 + 6
y = (x-1)^3 + 1
y = (x^2+1)^2 -1
y = -x^5 + 3x
A particle moves in a straight line with velocity v(t) = t^2. How far does the particle move between times t = 1 and t = 2?
-----------------------------------------------------
1/3
7/3
3
7
8
7/3
If y = cos^2 3x, then dy/dx =
-------------------------
-6 sin 3x cos 3x
-2 cos 3x
2 cos 3x
6 cos 3x
2 sin 3x cos 3x
-6 sin 3x cos 3x
The derivative of f(x) = (x^4)/3 - (x^5)/5 attains its max value at x =
---------------------------
-1
0
1
4/3
5/3
1
If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x^3 + k, then k is
-------------------------------------------
1/2
1/4
0
-1/8
-1/2
1/4
If f(x) = 2x^3 + Ax^2 + Bx - 5 and if f(2) = 3 and f(-2) = -37, what is the value of A+B?
--------------------------------------
-6
-3
-1
2
It cannot be determined from the info given
-1
The acceleration alpha of a body moving in a straight line is given in terms of time t by alpha = 8 - 6t. If the velocity of the body is 25 at t = 1 and if s(t) is the distance of the body from the origin at time t, what is s(4) - s(2)?
-----------------------------------------------
20
24
28
32
42
32
If f(x) = x^1/3(x-2)^2/3 for all x, then the domain of f' is
---------------------------------
{x|x=/0}
{x|x>0}
{x|0 <= x <= 2}
{x|x=/ 0 and x=/ 2}
{x|x is a real number}
{x| x =/ 0 and x=/ 2}
The area of the region bounded by the lines x = 0, x = 2, and y = 0 and the curve y = e^x/2 is
---------------------------
e-1/2
e-1
2(e-1)
2e-1
2e
2(e-1)
What is the area of the region completely bounded by the curve y = -x^2 + x + 6 and the line y = 4?
-------------------------
3/2
7/3
9/2
31/6
33/2
9/2
d/dx (arcsin 2x) =
-----------------------------
-1/2sqrt(1-4x^2)
-2/sqrt(4x^2-1)
1/2sqrt(1-4x^2)
2/sqrt(1-4x^2)
2/sqrt(4x^2-1)
2/sqrt(1-4x^2)
Suppose that f is a function that is defined for all real numbers. Which of the following conditions assures that f has an inverse function?
-------------------------
The function f is periodic

The graph of f is symmetric with respect to the y-axis

The graph of f is concave up

The function f is a strictly increasing function

The function f is continuous
The function f is a strictly increasing function
Given the function defined by f(x) 3x^5 - 20 x^3, find all values of x for which the graph of f is concave up
----------------------------------
x>0
-sqrt(2) < x < 0 or x > sqrt(2)
-2 < x < 0 or x > 2
x > sqrt(2)
-2 < x < 2
-sqrt(2) < x < 0 or x > sqrt(2)
lim of h -> 0 1/h ln(2+h/2) is
---------------------------------
e^2
1
1/2
0
nonexistent
1/2
Let f(x) = cos(arctan x ). What is the range of f?
-------------------------------------
{x|-pi/2 < x < pi/2}
{x|0 < x <= 1}
{x|0 <= x <=1}
{x|-1 < x < 1}
{x|-1 <= x <= 1}
{x|0<x<=1}
The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100pi square inches, what is the rate of increase, in cubic inches per second, in the volume V? (S = 4pir^2 and V = 4/3 pir^3)
-------------------------------------
10pi
12pi
22.5pi
25pi
30pi
30pi
A point moves in a straight line so that its distance at time t from a fixed point of the line is 8t-3t^2. What is the total distance covered by the point between t = 1 and t = 2?
---------------------------------------------
1
4/3
5/3
2
5
5/3
Let f(x) = |sin x -1/2|. The max value attained by f is
------------------------------------------
1/2
1
3/2
pi/2
3pi/2
3/2
If log a(2^a) = a/4, then a =
-----------------------
2
4
8
16
32
16
The region in the first quadrant bounded by the graph of y = sec x, x = pi/4, and both axes is rotated about the x-axis. What is the volume of the solid generated?
--------------------------------------
pi^2/4
pi - 1
pi
2pi
8pi/3
pi
If dy/dx = 4y and if y = 4 when x = 0, then y =
---------------------
4e^4x
e^4x
3 + e^4x
4 + e^4x
2x^2 + 4
4e^4x
The point on the curve 2y = x^2 nearest to (4,1) is
------------------
(0,0)
(2,2)
(sqrt(2),2)
(2sqrt(2),4)
(4,8)
(2,2)
If tan (xy) = x, then dy/dx =
-------------------------------------------
1 - y tan (xy) sec (xy)/x tan(xy) sec (xy)
sec^2(xy)-y/x
cos^2(xy)
cos^2(xy)/x
cos^2(xy)-y/x
cos^2(xy)-y/x
If the solutions of f(x) = 0 are -1 and 2, then the solutions of f(x/2) = 0 are
------------------------------------
-1 and 2
-1/2 and 5/2
-3/2 and 3/2
-1/2 and 1
-2 and 4
-2 and 4
For small values of h, the function ^4sqrt(16+h) is best approximated by which of the following?
-----------------------------------------
4 + h/32
2 + h/32
h/32
4 - h/32
2 - h/32
2 + h/32
f(x) = (2x + 1)^4, then the 4th derivative of f(x) at x = 0 is
------------------------
0
24
48
240
384
384
If y = 3/4+x^2, then dy/dx =
--------------------------
-6x/(4+x^2)^2
3x/(4+x^2)^2
6x/(4+x^2)^2
-3/(4+x^2)^2
3/2x
-6x/(4+x^2)^2
If dy/dx = cos(2x), then y =
-------------------------
-1/2 cos (2x) + C
-1/2 cos^2 (2x) + C
1/2 sin (2x) + C
1/2 sin^2 (2x) + C
-1/2 sin (2x) + C
1/2 sin (2x) + C
If f(x) = x, then f'(5) =
------------------------
0
1/5
1
5
25/2
1
The slope of the line tangent to the graph of y = ln(x/2) at x = 4 is
---------------
1/8
1/4
1/2
1
4
1/4
If y = 10^(x^2-1), then dy/dx =
------------------------------
(ln 10)10^(x^2-1)
(2x)10^(x^2-1)
(x^2-1)10^(x^2-2)
2x(ln 10)10^(x^2-1)
x^2(ln10)10^(x^2-1)
2x(ln 10)10^(x^2-1)
The position of a particle moving along a straight line at any time t is given by s(t) = t^2 + 4t + 4. What is the acceleration of the particle when t = 4?
--------------------------------
0
2
4
8
12
2
If f(g(x)) = ln(x^2+4), f(x) = ln (x^2), and g(x) > 0 for all real x, then g(x) =
------------------------------------
1/sqrt(x^2+4)
1/x^2+4
sqrt(x^2+4)
x^2+4
x+2
sqrt(x^2+4)
If x^2 + xy + y^3 = 0, then, in terms of x and y, dy/dx =
---------------------------------
-(2x+y/x+3y^2)
-(x+3y^2/2x+y)
-2x/1+3y^2
-2x/x+3y^2
-(2x+y/x+3y^2-1)
-(2x+y/x+3y^2)
The velocity of a particle moving on a line at time t is v = 3t^(1/2) + 5t^(3/2) meters per second. How many meters did the particle travel from t = 0 to t = 4?
------------------------------
32
40
64
80
184
80
The domain of the function defined by f(x) = ln (x^2-4) is the set of all real numbers x such that
--------------------------
|x|< 2
|x|<=2
|x|>2
|x|>=2
x is a real number
|x|>2
The function defined by f(x) = x^3 - 3x^2 for all real numbers x has a relative maximum at x=
-----------------------------
-2
0
1
2
4
0
If y = cos^2 x-sin^2 x, then y'
-------------------------------------
-1
0
-2sin(2x)
-2(cosx+sinx)
2(cosx-sinx)
-2sin(2x)
If f(x1) + f(x2) = f(x1+x2) for all real numbers x1 and x2 which of the following could define f?
--------------------------------------
f(x) = x+1
f(x)= 2x
f(x)= 1/x
f(x)= e^x
f(x)= x^2
f(x) = 2x
If y = arctan(cosx), then dy/dx =
---------------------------------
-sin x/1+cos^2x
-(arcsec(cosx))^2sinx
(arcsec(cosx))^2
1/(arccosx)^2 +1
1/1+cos^2 x
-sinx/1+cos^2x
If the domain of the function f given by f(x) = 1/1-x^2 is {x:|x|>1}, what is the range of f?
------------------------------
{x:-infinity < x < -1}
{x:-infinity < x < 0}
{x:-infinity < x < 1}
{x:-1 < x < infinity}
{x:0 < x < infinity}
{x:-infinity < x < 0}
d/dx(1/x^3 - 1/x + x^2) at x= -1 is
-----------------------------
-6
-4
0
2
6
-4
The graph of y^2 = x^2 + 9 is symmetric to which of the following?
I. The x-axis
II. The y-axis
III. The origin
----------------------------------------------
I only
II only
III only
I and II only
I, II, and III
I, II, and III
If the position of a particle on the x-axis at time t is -5t^2 then the average velocity of the particle for 0<= t <= 3 is
---------------------------------------
-45
-30
-15
-10
-5
-15
Which of the following functions are continuous for all real numbers x?
I. y=x^(2/3)
II. y=e^x
III. y=tanx
-------------------------------------
None
I only
II only
I and II
I and III
I and II
The volume of a cone of radius r and height h is given by V = 1/3 pir^2 h. If the radius and the height both increase at a constant rate of 1/2 centimeter per second, at what rate in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
---------------------------------
1/2pi
10pi
24pi
54pi
108pi
24pi
The area of the region in the first quadrant that is closed by the graphs of y = x^3 + 8 and y = x + 8 is
----------------------------------
1/4
1/2
3/4
1
65/4
1/4
The figure above shows the graph of a sine function for one complete period. Which of the following is an equation for the graph?
----------------------------------------
y = 2sin((pi/2)(x))
y = sin(pix)
y=2sin(2x)
y=2sin(pix)
y=sin(2x)
y=2sin(pix)
If f is a continuous function defined for all real numbers x and if the maximum value of f(x) is 5 and the min value of f(x) is -7, then which of the following must be true?
I. The max value of f(|x|) is 5
II. The max value of |f(x)| is 7
III. The max value of f(|x|) is 0
--------------------------------------------
I only
II only
I and II only
II and III only
I, II and III
II only
lim of x -> 0 (xcscx) is
----------------------------
-infinity
-1
0
1
infinity
1
If f(x) = lnx/x, for all x>0, which of the following is true?
------------------------------------
f is increasing for all x greater than 0
f is increasing for all x greater than 1
f is decreasing for all x between 0 and 1
f is decreasing for all x between 1 and e
f is decreasing for all x greater than e
f is decreasing for all x grether than e
An equation of the line tangent to y = x^3 + 3x^2 + 2 at its point of inflection is
-----------------------------------------
y= -6x - 6
y=-3x+1
y=2x +10
y=3x-1
y=4x+1
y=-3x+1
The average value of f(x) = x^2 sqrt(x^3+1) on the closed interval [0,2] is
-----------------------------------
26/9
13/3
26/3
13
26
26/9
The region enclosed by the graph of y=x^2, the line x=2, and the x-axis is revolved around the y-axis. The volume of the solid generated is
--------------------------------------------------
8pi
32/5 pi
16/3 pi
4pi
8/3 pi
8pi
If y = x^2e^x, then dy/dx =
-----------------
2xe^x
x(x+2e^x)
xe^x(x+2)
2x+e^x
2x+e
xe^x(x+2)
A particle with velocity at any time t given by v(t)=e^t moves in a straight line. How far does the particle move from t = 0 to t = 2?
----------------------------
e^2-1
e-1
2e
e^2
e^3/e
e^2-1
The graph of y=-5/x-2 is concave downward for all values of x such that
---------------------------
x<0
x<2
x<5
x>0
x>2
x>2
If y= lnx/x, then dy/dx =
---------------------------
1/x
1/x^2
ln x -1/x^2
1-lnx/x^2
1+lnx/x^2
1-lnx/x^2
The graph of y = f(x) is shown in the figure above. On which of the following intervals are dy/dx>0 and d^2y/dx^2 < 0?
I. a<x<b
II.b<x<c
III.c<x<d
--------------------------------
I only
II only
III only
I and II
II and III
II only
If x+2xy-y^2=2, then at the point (1,1), dy/dx is
--------------------------
3/2
1/2
0
-3/2
nonexistant
nonexistant
An equation of a line tangent to the graph of f(x) = x(1-2x)^3 t the point (1,-1) is
--------------------------------------------
y=-7x+6
y=-6x+5
y=-2x+1
y=2x-3
y=7x-8
y=-7x+6
If f(x) = sin x, then f'(pi/3) =
--------------------------
-1/2
1/2
sqrt(2)/2
sqrt(3)/2
sqrt(3)
1/2
If f(x) = sqrt(2x), then f'(2) =
---------------------------------
1/4
1/2
sqrt(2)/2
1
sqrt(2)
1/2
A particle moves along the x-axis so that at anytime t>= 0 its position is given by x(t) = t^3 - 3t^2 - 9t +1. For what values of t is the particle at rest?
--------------------------------------------
No values
1 only
3 only
5 only
1 and 3
3 only
If y = 2 cos(x/2), then d^2y/dx^2 =
-------------------------
-8cos(x/2)
-2cos(x/2)
-sin(x/2)
-cos(x/2)
-1/2cos(x/2)
-1/2cos(x/2)
Let f be a polynomial function with degree greater than 2. If a=/b and f(a) = f(b)=1, which of the following must be true for at least one value of x between a and b?
I. f(x)=0
II.f'(x)=0
III.f''(x)=0
---------------------------------
None
I only
II only
I and II only
I, II, and III
II only
If ln x - ln(1/x) = 2, then x =
----------------------
1/e^2
1/e
e
2e
e^2
e
If f'(x) = cos x and g'(x) = 1 for all x, and if f(0) = g(0) = 0, then lim of x -> 0 f(x)/g(x) is
---------------------
pi/2
1
0
-1
nonexistent
1
At x = 3, the function given by f(x) = x^2 , x<3 6x-9, x>=3
-------------------------------------
undefined
continuous but not differentiable
differentiable but not continuous
neither continuous nor differentiable
both continuous and differentiable
both continuous and differentiable
the lim of h -> 0 tan 3(x+h) - tan3x/h is
------------------------
0
3sec^2(3x)
sec^2(3x)
3cot(3x)
nonexistent
3sec^2(3x)
If f(x) = x/x+1, then the inverse function f^-1 is gven by f^-1(x) =
--------------------------
x-1/x
x+1/x
x/1-x
x/x+1
x
x/1-x
The absolute max value of f(x)=x^3-3x^2+12 on the closed interval [-2,4] occurs at x =
------------------
4
2
1
0
-2
4
4cos(x+pi/3) =
-----------
2sqrt(3) cosx - 2sinx
2cosx - 2sqrt(3) sinx
2cosx + 2sqrt(3) sinx
2sqrt(3)cosx + 2sinx
4cosx +2
2cosx - 2sqrt(3) sin x
f(x) = e^x sin x, then the number of zeros of f on the closed interval [0,2pi] is
---------------------
0
1
2
3
4
3
If lim of x -> 3 f(x)=7, which of the following must be true?
I. f is continuous at x=3
II. f is differentiable at x=3
III. f(3)7
-------------------------------
None
II only
III only
I and III only
I, II, and III
None
The graph of which the following equations has y =1 as an asymptote?
-------------------------------------
y=lnx
y=sinx
y=x/x+1
y=x^2/x-1
y=e^-x
y=x/x+1
The volume of the solid obtained by revolving the region enclosed by the ellipse x^2+9y^2=9 about the x-axis is
----------------------
2pi
4pi
6pi
9pi
12pi
4pi
Let f and g be odd functions. if p, r and s are nonzero functions defined as follows which must be odd?
I. p(x) = f(g(x))
II. r(x) = f(x) + g(x)
III. s(x) = f(x)g(x)
-------------------------
I only
II only
I and II only
II and III only
I, II, and III
I and II only
If x^3 + 3xy + 2y^3 = 17, then in terms of x and y, dy/dx
---------------------
-x^2+y/x+2y^2
-x^2+y/x+y^2
-x^2+y/x+2y
-x^2+y/2y^2
-x^2/1+2y^2
-x^2+y/x+2y^2
If the function f is continuous for all real numbers and if f(x) = x^2 - 4/x+2 when x=/ -2, then f(-2) =
--------------------
-4
-2
-1
0
2
-4
An equation of the line tangent to the graph of y = 2x +3/3x-2 at the point (1,5) is
-----------------------
13x - y =8
13x+y=18
x-13y=64
x+13y=66
-2x+3y=13
13x+y=18
If y = tan x - cot x, then dy/dx =
--------------------------
secxcsc
secx-cscx
secx+cscx
sec^2 x-csc^2 x
sec^2 x+csc^2 x
sec^2 x+csc^2 x
If h is the function given by h(x) = f(g(x)), where f(x)=3x^2 - 1 and g(x) = |x|, then h(x) =
--------------------------
3x^3 - |x|
|3x^2 - 1|
3x^2|x|-1
3|x|-1
3x^2-1
3x^2-1
f(x) = (x-1)^2 sin x, then f'(0) =
---------------
-2
-1
0
1
2
1
The acceleration of a particle moving along the x-axis at time t is given by a(t) = 6t - 2. If the velocity is 25 when t = 3 and the position is 10 when t=1, then the position x(t)=
-----------------------------
9t^2+1
3t^2-2t+4
t^3-t^2+4t+6
t^3-t^2+9t-20
36t^3-4t^2-77t+55
t^3-t^2+4t+6
The fundamental period of 2cos(3x) is
--------------------------
2pi/r
2pi
6pi
2
3
2pi/3
For what value of x does the function f(x)=(x-2)(x-3)^2 have a relative max?
---------------------
-3
-7/3
-5/2
7/3
5/2
7/3
If f(x) = sin (x/2), then there exists a number c in the interval pi/2 < x < 3pi/2 that satisfies the conclusion of the Mean Value Theorem. Which of the following could be c?
-------------------------------------
2pi/3
3pi/4
5pi/6
pi
3pi/2
pi