Jose Ramirez
Math 152 Section 26
Recitation Workshop 1
Question 5: Let R be the region bounded by the parabola y = x -
x 2 and the x-axis. Find he
equation of the line through the origin that divides R into two subregions of equal area.
To first approach
Jose Ramirez
Calculus 2 for Math and Physics
Section 26 Problems
Question 5: Find the area bounded by the curves y = sin(x) and y = cos(x) from x = 0 to x =
3 /4 .
First, to approach this problem what needs to be known is which function is at the top and
Jose Ramirez
Calc 152 workshop 8
Section 26
Question 4 Each of the following sequences has a limit 0:
cfw_ cfw_ cfw_ cfw_
1 1 1
1
2
n n=1 n n=1 n n=1 10n n=1
For each sequence, state exactly how large n must be to ensure that the term an of the
4
8
s
Jose Ramirez
Math 152 Workshop 4
Section 26
1. Calculate the area within the two ellipses
x2 2
+ y =1 and
3
y2 2
+ x =1 .
3
To begin this problem, we have to put everything in terms of one variable. Since both equations
have both the x and y variables on
Jose Ramirez
Workshop 05
Section 26
1.) The region R is bounded below by the x-axis, bounded on the left by the line x = 1, bounded
5+ x
on the right by the line x = 2, and bounded above by the curve y= x 2+ 4 x +3 .
a. Sketch the region R and set up a de
Jose Ramirez
Calculus 152 Section 26
Workshop 6
Question 1: Determine whether each of the following integrals is convergent or divergent.
Evaluate those that are convergent. Be sure to show your work and explain your reasoning.
1
a.) xln ( x )2 dx
e
b.)
2
Jose Ramirez
Calc 152 Workshop 7
Section 26
cos
Question 1: Suppose f is defined by f(x) = 3 e ( x) . Maple produced graphs of f and its for
derivatives on the interval [2,7]. The graph of f is to the right, and the graphs of the first four
7
derivatives
Jose Ramirez
Math 152 Section 26
Recitation Workshop 1
Question 5: Find the area bounded by the curves y = sin(x) and y = cos(x) from x = 0 to x =
3 /4 .
First, to approach this problem what needs to be known is which function is at the top and which
is a
Jose Ramirez
Math 152 Section 26
Recitation Workshop 3 Volumes of Revolution
Question 3: Let R be the region enclosed by the curves y = ln(x), y = 0, x = 1 and x = e. Find the
area R, the volume resulting if R is revolved about the x-axis, and the volume
1/31/2017
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Discrete Mathematics: Introduction to Mathematical Reasoning, 1e
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1/31/2017 Discrete Mathematics: Introduction to Mathematical Reasoning, 1e
PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without
publisher's prior permission. Viol
1/31/2017
PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without
Discrete Mathematics: Introduction to Mathematical Reasoning, 1e
publisher's prior permission. Viol
1/31/2017
PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without
Discrete Mathematics: Introduction to Mathematical Reasoning, 1e
publisher's prior permission. Viol
1/31/2017
PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without
Discrete Mathematics: Introduction to Mathematical Reasoning, 1e
publisher's prior permission. Viol
1/31/2017 Discrete Mathematics: Introduction to Mathematical Reasoning, 1e
PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without
publisher's prior permission. Viol
Direct proof:
a. If n is odd then
n
2
is odd.
1. Show that the product of any two odd integers is odd.
2. The sum of any two rational numbers is rational
3. Let a, b, c integers. Show that if a divides b and a divides c, then a divides (b+c)
Contradiction
Relations:
1. In a certain community, every individual has a phone. A relationR is defined on
this community such that aR b iff a had a phone conversation with b.
a. Is the relationR symmetric? Explain
b. Is the relation R transitive? Explain
2. In the se
Test4 Review
Functions
1-
Explain what it means for a function to be one to one. Give an example (you can use a diagram)
If there is an image k has a pre-image, then that pre-image is unique.
Onto function:
Every elemet in the set has a pre-image.
2-
Is t
Math 250 Linear Algebra with MATLAB, Quiz #3
Answer the questions in the spaces provided and label all of your work. Responses with no
work may receive no credit even if the answer is correct.
Name:
1. Suppose A is a m n matrix. The P LU -decomposition of
Math 250 Linear Algebra with MATLAB, Quiz #2
Answer the questions in the spaces provided and label all of your work. Responses with no
work may receive no credit even if the answer is correct.
Name:
1. Let S = cfw_u, v, w be a set of three vectors in Rn .
Math 250 Linear Algebra with MATLAB, Quiz #1 Solutions
Answer the questions in the spaces provided and label all of your work. Responses with no
work may receive no credit even if the answer is correct.
Name:
1. Consider the following matrix.
0
A= 2
3
1 2
Math 250 Linear Algebra with MATLAB, Quiz #4
Answer the questions in the spaces provided and label all of your work. Responses with no
work may receive no credit even if the answer is correct.
Name:
1. Consider the matrix A below,
5 1
4
A= 0
0
2
along wit
revised 1/16/17
Spring 2017
MATH 250 Introduction to Linear Algebra with MATLAB, Section C2
Text: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach, 2nd Edition
ISBN # 978-0-13-187141-0, Prentice-Hall, Upper Saddle River, NJ 07458
Syl
MATH 244
QUIZ 5
Name:
Section:
Show your work and clearly label your answer.
(1) Find the general solution, and then the specific solution to the IVP:
2y 00 + 2y 0 4y = 0
y(0) = 0,
y 0 (0) = 1
Solution: The characteristic equation reads:
2r2 + 2r 4 = 0
wh
MATH 244
QUIZ 2
Name:
Section:
Show your work
(1) (a) Find the (unique) solution to this problem:
y 0 = 4ty 2
y(0) = y0
where y0 > 0
Solution: This equation is seperable. Separating variables gives us
dy/y 2 = 4tdt
Thus, we can integrate both sides to obt