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Compute
.
Compute
.
What type of function is
f (x) = x
^{6}
?
What type of function is
f (x) = x
^{3} + 3x
?
What type of function is
f (x) =
x
?
For the following function, what value must be assigned to
f (3)
to
make the function continuous at
x = 3
?
f (x) =


A general expression for the derivative of
f (x)
is:
What is the derivative of
f (x) =
Π
^{4}
?
What is the derivative of
f (x) = ?
For the function
f (x) = x
^{2}  4x + 5
, give the equation of the tangent at
x = 3
.
Find the equation of the line normal to the tangent of
f (x) = x
^{2}  4x + 5
at
x = 1
.
Compute
where
x = 4x
^{2}
y  2y
.
Car A and Car B start at the same point. At time
t = 0
, Car A travels
south at 40 miles per hour. Car B travels west at 20 miles per
hour. At what rate is the distance between the two cars changing at
t = 3
hours?
The momentum of an object is given by the relation
p = mv
, where
m
=mass and
v
=velocity. If an object weighing
3
kg accelerates at
2
m/s
^{2}
, what is the rate of change of its momentum?
The position of an object is represented by
s(t) = t
^{2}  t  1
. What is
the object's velocity at
t = 3
seconds?
If the position of an object is represented by the equation
s(t) = t
^{2}  t  1
, what is the total distance traveled between
t = 0
and
t = 2
?
Find a number
c
on
[a, b]
such that
f'(c) =
where
f (x) = 2x
^{2}
and
[a, b] = [ 1, 2]
For the function
f (x) = x
^{3}
, is the critical point at
x = 0
a local
maximum, local minimum or neither?
Find the inflection points on the interval
[ ,]
for the function
f (x) = sin(x)
.
Does
f (x) =
have a horizontal asymptote?
Sophia is standing
1000
feet away from the base of a tall
building. At time
t = 0
, she sees a baby drop from the roof of that
building and calculates that it will hit the ground in
21
seconds. Her normal running speed is
10
feet per second, but she can
increase her speed by
10
feet per second with each apple she
eats. If it takes her one second to eat an apple, how many apples
should she eat in order to minimize the total time it will take
(eating + running) to get to the base of the building?
A triangle has two sides that are each 5 cm long. What angle between
the two sides will maximize the triangle's area?
Let
F(x) = x
^{4}  2x
. What kind of point occurs at
x = 3
?
What is the derivative of
f (x) =
?
Evaluate
7dx
.
Evaluate
sin(7x+17)dx
.
Evaluate cos(Πx)dx.
Evaluate
t
dt
Using left endpoints and 4 rectangles, approximate
x
^{2}
dx
.
Using right endpoints and 4 rectangles, approximate
x
^{2}
dx
.
Evaluate
sin(x)dx
.
The velocity of a particle is given by the equation
v(t) = t
^{3}  2
. What
is the total change in position from
t = 0
to
t = 2
?
What is the average value of
f (x) = 11x
^{2}  2
on [1,1]?
What is the average value of
f (x) =
on
[0, 2Π]
?
Compute
sin(t
^{4})dt
.
Evaluate
cos(t+4)dt
.
Using 4 trapezoids, approximate
x
^{2}
dx
.
If
f (x) = x
^{3}
, compute
f
^{1}
(2)
.
Evaluate
x
^{
Π
}
.
Evaluate
x
^{x}
.
What is the rate constant of a substance that decays 27\% after 20 minutes?
If
= 7y
, what is a possible equation for the corresponding function?
Evaluate
dx
.
Evaluate
e
^{3x}
dx
.
Evaluate
log_{7}(56)  log_{7}(8)
.
Evaluate
7^{x}
dx
.