Math 152 (21-23): Workshop 1
September 11, 2015
1-1. Sketch the region R defined by 1 x 2 and 0 y 1/x3 .
a) Find (exactly) the number a such that the line x = a divides R into two parts of equal area.
Sample Homework Write-Up - Excellent
Problem: A fa.rmerhas 200 feet of fencingto make a rectangula,rpen. What are the length and width
of the largestarea pen that she can make with her fencing?
Let x:
Challenge Problems Exam 1
1. (a) State the Mean Value Theorem, making sure you clearly state the hypotheses and the conclusion.
(b) Show that if F (x) and G(x) are antiderivatives of f (x), then F (x)
Economics Applications Homework
1. Suppose a company can produce a product for $500 a piece. They have 20 potential customers,
each interested in buying a single item. There are 6 that are willing to
Series Problems Fun Pack !
I. Do the series below converge or diverge? What test would you use? Find the sum of each series when reasonable.
X
n
3
n +1
n=1
13.
X
(1)n n
2.
n+1
n=1
14.
1.
X
cos(3n)
3.
Integration Problems Fun Pack !
I. Evaluate the integrals below, clearly noting which integration technique(s) you use in your solution. If the
integral is improper, say so, and either give its value
Beginning Differential Equations Homework
1. Verify that the function y(x) = e3x is a solution to the DE y 00 + 2y 0 3y = 0
2. Verify that the function y(x) =
ln x
is a solution to the DE x2 y 00 + 5x
640:152 Calculus II, Midterm Exam #1, Spring 2015
Department of Mathematics, Rutgers University
NAME (PLEASE PRINT): KEY
SIGNATURE:
INSTRUCTOR: Nathan Corwin
SECTION: (circle one)
01
02
03
07
08
09
In
640:152 Calculus II, Midterm Exam #2, Spring 2015
Department of Mathematics, Rutgers University
NAME (PLEASE PRINT): Solutions
SIGNATURE:
INSTRUCTOR: Nathan Corwin
SECTION: (circle one)
01
02
03
07
08
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EXPOS * Basic Composition * EAD I/II * Research in the Disciplines & 301 *
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Review sheet for Exam 1 of Math 152
These problems are presented in order to help you understand the material
that is listed prior to the first exam in the syllabus. DO NOT assume that
your first midt
Math 152: Calculus II, Spring 2017
Professor: Oliver Pechenik
Email: [email protected]
Office: Hill Center 205
Office Hours: Tuesday 1:302:30, Thursday 910
Course Meetings: TF 8:4010, HLL 1
Hyperbolic Functions
Recall: Trigonometric Functions.
The basic trigonometric functions are the sine and the cosine functions. We use them to get the
other four trigonometric function:
tan =
sin
,
co
Algebra / Trig / Calculus I Review
Critically important: You absolutely must be able to do the following types of problems in order
to succeed in this course. If you are unsure of any of these, you sh
640:152 Calculus II, Spring 2012
Final Examination
Department of Mathematics, Rutgers University
NAME (PLEASE PRINT):
SIGNATURE:
RUTGERS ID #:
INSTRUCTOR & SECTION:
Instructions:
Turn off and put awa
640:152 Calculus II, Midterm Exam #2, Spring 2014
Department of Mathematics, Rutgers University
NAME (PLEASE PRINT):
SIGNATURE:
INSTRUCTOR: Dr. Nikolaev
SECTION:
Instructions:
Turn off and put away a
Volumes
A. Consider the region bounded by the graphs of
and
Find the volume of the solid obtained by rotating the above region about the following axes. Find
the volume twice each time: first using th
Final Exam Review Questions Part 1.
Area between curves- Volumes- Average Value-integration by parts-improper integral- parametric-polardifferential equation
1. The base of a solid is the region insid
MATH 152 REVIEW
Area between curves: Find intersection point (unless a, b given), find top function f(x), bottom function g(x)
function is with respect to y, find right function f(y), and left functio
2/4/2015
TECHNIQUES OF INTEGRATION
Due to the Fundamental Theorem of Calculus
7
(FTC), we can integrate a function if we know
an antiderivative, that is, an indefinite integral.
TECHNIQUES OF INTEGRAT
Math 152 Workshop 6
1
Z
xk (1 x)l dx.
Problem 1. Let k, l be nonnegative integers, and let I(k, l) =
0
a) Show that I(k, l) = I(l, k).
b) Find I(k, 0) and I(0, k)
c) For k > 0, prove that I(k, l) =
k
Math 152(01-03): Workshop 4
October 19, 2016
4-1. Suppose f (x) = x ln x .
a) Verify that lim+ f (x) = 0 and lim f (x) = 0. Graph f on the interval [0, 10].
x
x0
x2
b) A remarkable result of third se
152 Review problems for exam 2
Try to do all the problems before you watch the video solution.
1. (a) Find the 4th Maclaurin polynomial of the function f (x) = e2x .
(b) Use (a) to approximate e0.2
(c
Summary of Convergence and Divergence Tests for Series
Test
nth -term
Series
Convergence or Divergence
Comments
X
Diverges if lim an 6= 0
Inconclusive if lim an = 0
an
Geometric
Series
n
n
(i) Converg
Math. 152, Additional review problems for exam 2.
1. Find the limit of each of the given the sequences.
(
(a) an = 1 +
3
2n
)4n
sin2 n
n3
(b) bn =
2. Find the exact sum of each of the given series.
(a