Math 157
Exam 3 Compressed
3
December 11, 2013
2
1. Find the absolute maximum and minimum values of f (x) = x 6x + 9x + 2 over the interval [0, 2].
2. Find the absolute maximum and absolute minimum values of f (x) =
3. Sketch the graph of f (x) =
x
1+x2 .
Name(s):
Math 157
The Fundamental Theorem of Calculus
November 19, 2013
Figure 1: y = 2t3 11t2 + 17t 6
2t3 11t2 + 17t 6 dt.
1. Evaluate the indenite integral
Solution.
1 4 11 3 17 2
t t + t 6t + C
2
3
2
2. Refer to the graph above while evaluating the fol
Math 157
Final Exam Practice ProblemsSolutions
December 17, 2013
1. Find the limit (either a number, , or ) or explain why it does not exist: lim+
x1
x2
1 x2
Solution.
6x2 x + 1
x 2x2 + 7x
2. Find the limit (either a number, , or ) or explain why it does
Math 157
Exam 3
April 2, 2012
Name:
Instructions: Calculators, notes, cell phones, or other materials are not permitted. Show all your work:
even correct answers may receive little or no credit if a method of solution is not shown.
1. Sketch the graph of
Math 157
Exam 1 Compressed
December 11, 2013
4x + 8
x2 x2 + 2x
x
2. Find the limit (either a number, , or ) or explain why it does not exist: lim+
x2 4 x2
1. Find the limit (either a number, , or ) or explain why it does not exist: lim
x2
x x + 5
9h3
4. F
Math 157
Exam 2 Compressed
December 11, 2013
1. Use the denition of the derivative to calculate f (1) for f (x) = (x + 1)2 .
2. The position of a particle at time t is given by s(t) = 2t2 12t + 8. When is the velocity of the particle equal to zero?
3. Die