MATH 20515
Exam #1
This test is closed-book and closed-notes. No calculator is allowed for this test. When answering
the questions you are only allowed to use tools and techniques that we have discussed up to this
point, i.e. no advanced dierentiation tec
MATH 20515
Quiz #1 Solutions
Name:
1. (4 points) Identify the domain of the following functions:
(a) (2 points) g (t) = 3t 2.
The obvious impediment to the existence of this function is when 3t 2 is negtive,
since square roots of negative numbers are spec
MATH 20515
Quiz #2
Sample for distribution
1. (4 points) For the plot of g (x) shown below, indicate whether or not each of the
following quantities can be evaluated. If they can be evaluated, compute their values.
If they cannot be evaluated, explain why
MATH 20515
Quiz #1
Sample for distribution
1. (4 points) Identify the domain of the following functions:
(a) (2 points) g (t) = 3t 2.
(b) (2 points) f (x) =
4x
.
2x 1
2. (4 points) Sunspot intensity uctuates over an 11-year cycle. The average radiance of
MATH 20515
Practice Exam #2 Solutinos
1. (8 points) The horizontal displacement in meters of a particle at time t, measured in seconds, is given by the formula s(t) = t3 - 8t2 + 16t. (a) (2 points) What is the particle's velocity after 2 seconds? The velo
MATH 20515
Practice Exam #1
This test is closed-book and closed-notes. No calculator is allowed for this test. When answering
the questions you are only allowed to use tools and techniques that we have discussed up to this
point, i.e. no advanced dierenti
MATH 20515
Practice Exam #2
This test is closed-book and closed-notes. No calculator is allowed for this test. For full credit
show all of your work (legibly!), unless otherwise specied.
For the purposes of this exam, all answers must be in terms of famil
MATH 20515
Quiz #2 solutions
1. (4 points) For the plot of g (x) shown below, indicate whether or not each of the
following quantities can be evaluated. If they can be evaluated, compute their values.
If they cannot be evaluated, explain why.
4
3
2
1
3
2
MATH 20515
Quiz #3
1. (8 points) Solve the problems given below. (a) (4 points) Given f (x) = (x5 + ex )(x + 3), find f (x).
(b) (4 points) Find
d t2 -1 . dt et
2. (4 points) Determine the values of the following limits if possible; if they can not be eva
MATH 20515
Quiz #6
1. (6 points) Evaluate the following limits, or demonstrate that they do not exist: (a) (2 points) lim cos-1 . 2
0
(b) (2 points) lim
ex . x+2 x2
(c) (2 points) lim xe-x .
x
2. (8 points) You must print a small poster with 200 square in
MATH 20515
Quiz #6 Solutions
1. (6 points) Evaluate the following limits, or demonstrate that they do not exist:
(a) (2 points) lim cos1 .
2
0
We note that, evaluated at = 0, the expressions cos 1 and 2 are both zero;
0
thus, our limit involves a 0 indete
MATH 20515
Quiz #5
1. (6 points) Liquids in microgravity tend to form perfect spheres, and a sphere or radius
4
r has volume 3 r3 . A scientist on the international space station is sipping at a sphere
of orange juice, drinking 3 cubic centimeters per sec
MATH 20515
Quiz #5
1. (6 points) Liquids in microgravity tend to form perfect spheres, and a sphere or radius
r has volume 4 r3 . A scientist on the international space station is sipping at a sphere
3
of orange juice, drinking 3 cubic centimeters per sec
MATH 20515
Quiz #3 solutions
1. (8 points) Solve the problems given below.
(a) (4 points) Given f (x) = (x5 + ex )(x + 3), nd f (x).
d
f (x) = dx [(x5 + ex )(x + 3)], which we can evaluate using the product rule:
d
(x5 + ex )(x + 3)
dx
d
d5
(x + ex ) (x +
MATH 20515
Quiz #4
1. (14 points) Answer the questions below: (a) (5 points) Find
d d
(cos )esec .
(b) (4 points) For g(t) = arctan(t ln t), find g (t).
(c) (5 points) Given that y = earcsin(t ) , find
2
dy . dt
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Thursday, October 16, 2008
MATH 20515
MATH 20515
Quiz #4 solutions
1. (14 points) Answer the questions below:
d (a) (5 points) Find d (cos )esec . Using the product rule:
d (cos )esec = d
d sec d d sec cos esec +(cos ) e = - sin esec +(cos ) e d d d
Finding the derivative of esec , however, w