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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
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ln(x-2) < 0
------------------ x < 3 0 < x < 3 2 < x <3 x > 2 x > 3 |
2 < x < 3
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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
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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
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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
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For what value of k will x + k/x have a relative max at x = -2
------------------------------------------- - 4 - 2 2 4 None of these |
4
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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
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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
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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
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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}
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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)
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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
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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)
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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
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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
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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
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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
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d/dx (ln e^2x) =
----------------------- 1/e^2x 2/e^2x 2x 1 2 |
2
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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)
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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the fundamental period of the function defined by
f(x) = 3 - 2cos^2 (pi x/3) is --------------------------------------------------- 1 2 3 5 6 |
3
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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
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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
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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
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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
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If f(x) = x - 1/ x + 1 for all x=/ 1, then f'(1)
------------------------------- -1 -1/2 0 1/2 1 |
1/2
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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
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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
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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
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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
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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
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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
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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
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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}
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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)
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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
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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)
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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
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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)
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lim of h -> 0 1/h ln(2+h/2) is
--------------------------------- e^2 1 1/2 0 nonexistent |
1/2
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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}
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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
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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
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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
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If log a(2^a) = a/4, then a =
----------------------- 2 4 8 16 32 |
16
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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
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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
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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)
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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
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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
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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
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f(x) = (2x + 1)^4, then the 4th derivative of f(x) at x = 0 is
------------------------ 0 24 48 240 384 |
384
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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
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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
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If f(x) = x, then f'(5) =
------------------------ 0 1/5 1 5 25/2 |
1
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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
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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)
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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
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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)
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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)
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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
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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
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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
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If y = cos^2 x-sin^2 x, then y'
------------------------------------- -1 0 -2sin(2x) -2(cosx+sinx) 2(cosx-sinx) |
-2sin(2x)
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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
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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
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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}
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d/dx(1/x^3 - 1/x + x^2) at x= -1 is
----------------------------- -6 -4 0 2 6 |
-4
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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
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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
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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
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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
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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
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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)
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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
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lim of x -> 0 (xcscx) is
---------------------------- -infinity -1 0 1 infinity |
1
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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If x+2xy-y^2=2, then at the point (1,1), dy/dx is
-------------------------- 3/2 1/2 0 -3/2 nonexistant |
nonexistant
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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
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If f(x) = sin x, then f'(pi/3) =
-------------------------- -1/2 1/2 sqrt(2)/2 sqrt(3)/2 sqrt(3) |
1/2
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If f(x) = sqrt(2x), then f'(2) =
--------------------------------- 1/4 1/2 sqrt(2)/2 1 sqrt(2) |
1/2
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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
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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)
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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
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If ln x - ln(1/x) = 2, then x =
---------------------- 1/e^2 1/e e 2e e^2 |
e
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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f(x) = (x-1)^2 sin x, then f'(0) =
--------------- -2 -1 0 1 2 |
1
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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
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The fundamental period of 2cos(3x) is
-------------------------- 2pi/r 2pi 6pi 2 3 |
2pi/3
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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
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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
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