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Let
f (x) =
x)
for
x > 0
, and
f (x) = 0
for
x≤ 0
. Which of
the following is true?
Compute
.
Let
g(x) = 1/x
(with domain
| x| > 0
). Which of the following statements is true of
g
?
The function
f (x) = sin(x)
is invertible when defined on which of the following
domains?
What is the value of
x sin(1/x)
?
Let
f (x) = ax + b
. The inverse function of
f (x)
has slope
Let
f (x) = x
^{2}
for
x≠1
and let
f (1) = 2
. Then
f (x)
equals
The degree of the product of two degree
3
polynomials is equal to
Which of the following points is equal to the image of some real number in the domain of
the function
f (x) = 2 sin(2x)
?
The inverse function of
f (x) = (1/3)e
^{2x}
is
Find the derivative of
sin(e
^{x})
.
Compute the derivative of
.
Find the derivative of
cos(sin(x)))
.
Compute the derivative of
25x
^{2} + 4
.
What is the derivative of
log x
?
What is the derivative of
| x|
at
x = 0
?
Find the derivative of
e
^{2x+1}
.
Compute the derivative of
1/(x
^{2} + 1)
.
What is the derivative of
at
x = 1/2
?
Find the third derivative of
f (x) = 2 sin(3x)
.
What is the derivative of
tan(x)
at
x = Π/2
?
Compute the derivative of
f (x) = (x
^{2} +1)log x
.
Find
f'(x)
, where
f (x) = e
^{-x} + x
.
Compute the derivative of
x
^{3} + x + 1/x + 1/x
^{3}
.
Find the values of
x
at all the critical points
f (x) = x
^{3}/3 - x
^{2} + x
.
Find the derivative of
1/tan(x)
.
What is the minimum value of
e
^{x} - x
?
Find the maximum value of
sin(x) + cos(x)
.
Find the minimum value of
x
^{2} - 6x + 11
on the interval
[2, 5]
.
Find all values of
x
at which the derivative of
f (x) = log| x| - x
is zero.
Use implicit differentiation to find the slope of the tangent line to the graph
of the equation
x
^{2}
y
^{4} = 2x
^{2} + y
at the point
(1, - 1)
.
Which of the following is an antiderivative of
-1/x
^{2}
?
What is the
y
-intercept of the tangent line to the graph of
x
^{2}
at
x = 3
?
Find the second derivative of
x log x
.
What is the
x
-intercept of the tangent line to the graph of
e
^{x}
at
x = 0
?
Compute the maximum vertical distance between the graphs of
cos(x)
and
sin(x)
.
If an ostrich's velocity at time
t
is given by
log(t
^{2})
, what is the ostrich's
acceleration at time
t = 4
?
What are the values of
x
at inflection points of
x
^{3} -3x
^{2} + x + 1
?
Compute
L
_{2}(sin(x), - Π, 0)
.
Find
L
_{4}(sin(x), - Π, 0)
.
Compute
4x
^{3}
dx
.
Find
cos(x)x
.
Compute
(1/x)dx
.
Find the upper Riemann sum
U
_{48}(5, 1, 2)
.
Compute
(1 - cos^{2}(x))dx + (- sin^{2}(x))dx
.
Which of the following is an antiderivative of
4(x + 1)^{3}
?
Find
t
^{2} - 1dt
.
Compute
sin(2x)dx
.
What is
(- 1/x
^{2})dx
?
The term 'indefinite integral' is equivalent to which of the following terms?