Math 261
Exam 4
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem will be prop
Math 261 - Lab 16
The Second Derivative and Curve Sketching
Name:
Show all work for credit.
1. Assume that the given graph is the derivative, f , of a continuous function f .
(a) Identify the critical
Math 261
Quiz 1
08/26/2013
Name:
1. Johann Bernoulli is famous for his contributions to mathematics.
(a) Give the name of the city where Johann Bernoulli was born and the year he was born.
(b) Describ
Math 261
Exam 3
11/06/2013
Name:
Instructions: You will have 55 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem w
Math 261
Final Exam - Practice Problem Solutions
1. A function f is graphed below.
f(x)
6
5
4
3
2
1
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
(a) Find f (0), f (2), f (1), and f (4)
f (0) = 3; f (
Math 261
Numerical Integration Handout
Recall: When we rst dened the denite integral, we did so using the idea of a Riemann sum. Each Riemann sum
corresponds to approximating the area between a functi
Math 261
The Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus Part 1:
x
f (t) dt for every x in [a, b] is continuous on
Let f be a continuous function on the interval [a, b], then F
Math 261 Lab 22
Conic Sections Part 2
Name_
Show all work for credit. Also, give exact answers unless otherwise noted.
1.
Find an equation of the given hyperbola with the given
foci.
2.
Find an equa
Math 261
Exam 1 - Practice Problem Solutions
1. Given the points A : (4, 2) and B : (2, 7):
(a) Find an equation for the line containing A and B
7 (2)
9
3
y2 y1
=
=
= .
m=
x2 x1
2 4
6
2
3
Using the po
Math 261
Exam 4 - Practice Problem
Solutions
1. Suppose you throw a ball vertically upward. If you release the ball 7 feet above the ground at an
initial speed of 48 feet per second, how high will the
Math 261
Exam 3 - Practice Problems
1. The graph of f is given below. Answer the following questions.
(a) Find the intervals where f is increasing: (6, 4),
(1, 1), (3, 5), (6, )
(b) Find the intervals
Math 261
Final Exam - Practice Problem Solutions
1. A function f is graphed below.
f(x)
6
5
4
3
2
1
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
(a) Find f (0), f (2), f (1), and f (4)
f (0) = 3; f (
Math 261
Exam 2 - Practice Problems
1. Find the derivative y =
dy
dx
for each of the following:
(a) y = 2 x + x2
y = 2 + 2x
(b) y = cot x
y = csc2 x
(c) y = x sec(x2 )
1
1
1
y = 2 x 2 sec(x2 ) + x 2 s
Math 261 Lab 21
Conic Sections Part 1
Name_
Show all work for credit. Also, give exact answers unless otherwise noted.
1.
Find an equation of the given parabola where the focus and
vertex are shown.
y
Math 261
Exam 3
06/05/2012
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem w
Math 261
Exam 2
05/29/2012
Name:
Instructions: You will have 60 minutes to complete this exam. Calculators are allowed, but no other references. The credit
given will be proportional to the amount of
Math 261
Exam 4 Solutions
Name:
Instructions: You will have 60 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem wi
Math 261
Exam 4 - Version 1
Solutions
Name:
Instructions: You will have 55 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on eac
Math 261
Exam 1
Version 1
Name:
Instructions: You will have 55 minutes to complete this exam. Non-graphing Calculators are allowed, but this is a closed
book, closed notes exam. The credit given on ea
Math 261
Exam 2 - Version 1
Name:
Instructions: You will have 55 minutes to complete this exam. Calculators are allowed, but no other references. The credit
given will be proportional to the amount of
Math 261
Exam 1 - Practice Problem Solutions
1. Given the points A : (4, 2) and B : (2, 7):
(a) Find an equation for the line containing A and B
7 (2)
9
3
y2 y1
=
=
= .
m=
x2 x1
2 4
6
2
3
Using the po
Math 261
Exam 3
03/21/2008
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a closed book, closed
notes exam. The credit given on each problem w
Math 261
Exam 2 Solutions
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but no other references. The credit
given will be proportional to the amount of c
Math 261
Exam 1 - Solutions
Instructions: You will have 60 minutes to complete this exam. Calculators are allowed, but this is a closed
book, closed notes exam. The credit given on each problem will b
Math 261
Exam 1 Makeup Problem
Due: Monday 2/04/2008
Name:
1. (5 points) Use the Intermediate Value Theorem to prove that the function f (x) = x3 15x + 1 has at least
three zeros in the interval [4, 4
Math 261
Exam 2 - Practice Problems
1. Find the derivative y =
dy
dx
for each of the following:
(a) y = e2 x + ex2
y = e2 + 2ex
(b) y = cot x
y = csc2 x
(c) y = x sec(x2 )
1
1
1
y = 2 x 2 sec(x2 ) + x
Math 261
Exam 2 - Practice Problems
1. Find the derivative y =
dy
dx
for each of the following:
(a) y = e2 x + ex2
(b) y = cot x
(c) y = x sec(x2 )
(d) y = 2 tan3 (2x3 )
x2 7 cos(3x)
(e) y =
x + sin(3
Math 261
Exam 4 - Practice Problems
1. Suppose you throw a ball vertically upward. If you release the ball 7 feet above the ground at an
initial speed of 48 feet per second, how high will the ball tra
Math 261
Final Exam - Practice Problem Solutions
1. A function f is graphed below.
f(x)
6
5
4
3
2
1
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
x
1
2
3
4
5
6
(a) Find f (0), f (2), f (1), and f (4)
f (0) = 3; f (
Math 261
Exam 4 - Practice Problems
Solutions
1. Suppose you throw a ball vertically upward. If you release the ball 7 feet above the ground at an
initial speed of 48 feet per second, how high will th