Rogawski Calculus, Early Transcendentals Applications Index
Chapter 1: Precalculus Review
Application Astronomy Description Escape Velocity from a Planet with Regards to Mass, Radius, and Universal Gravitational Constant Velocity of Electron Emitted from
CALCULUS III
15-MATH-252-006 Spring, 2008.
J. M. Osterburg, Professor of Mathematical Sciences McMicken College of Arts & Sciences University of Cincinnati March 31, 2008
How to nd me : 821-D, Old Chemistry Bldg.:
(
513.556.4099
james.osterburg@uc.edu Oc
Finding Sequences to Squeeze
n n + n1/n
and Hence, to Compute lim
n n + n1/n
n
+L'H^pital's Rule Does Work o
JO
We have proven
n
lim n1/n = 1.
This means that for any > 0 there is a positive integer M such that if n M then |n1/n - 1| . I don't need to wor
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1. A) B) C) D)
2. Q.16 (Sec 10.6) Find the exact intervals on which the following series converge: A) B) C)
3. Q.2 (Sec 10.6) The values of A) B) C) D) E) for which the series converges are:
4. Q.11 (Sec 10.5) Use the Root Test to determin
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1. Q.1 (Sec 12.1) Let . Find the vector
such that
.
2. Q.2 (Sec 12.1) Let
. Calculate:
3. Q.3 (Sec 12.1) Find for which
is parallel to
where
4. Q.4 (Sec 12.2) A) Find the vector equation of the line which is parallel to the vector passes t
Name: _ Date: _
1. Q.1 (Sec 10.1) Let be a positive sequence such that .
The following statement holds: A) The sequence is decreasing but does not converge. B) The sequence is decreasing and converging to . C) The sequence is increasing and diverging. D)
INTEGRATION E STRATEGIES
T
he set of exercises in this section consists of an assortment of indenite integrals that can be evaluated using the techniques developed in Chapter 7. Your task is to decide which techniques are best suited to the given integral
Extra Credit- Calculus III Name:
Due, May 30, 11 AM. Just 4 of the following problems will be graded and they will be chosen on May 30. Each graded problem will count 25 points no matter what the test says. Problems #6 & # 8 now must be done. Remember thi
Divergence test If the limnan0 then the series an diverges. If limnan=0 then the divergence test fails Geometric Series Test The series n=0rn converges if |r|<1. Diverges otherwise. Convergence of Geometric Series To determine what each geometric series c
STRATEGIES FOR F TESTIN G SERIES
The Basic Tests for Innite Series (A) Divergence Test (B) Integral Test (C) Comparison Test (D) Limit Comparison Test (E) Ratio and Root Tests (F) Leibniz Test for Alternating Series
e have considered many basic convergenc