CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 1.
Due January 15.
1.1. Formulate and prove a statement similar to Lemma 1.8 for the case when f (x0 ) < 0. (See Lecture 1 of the Course Notes). 1.2. Give
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 11.
Due April 9.
11.1. Find the equation of the tangent line to the parametric curve given by x = 3t2 + 1 y = 2t3 + 1, that passes through the point (4, 3
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 10.
Due April 5.
10.1. Find the Maclaurin series for f (x). Find the radius of convergence of the series, and show, using Lagranges remainder theorem that
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 9.
Due March 26.
9.1. Find the radius and the interval of convergence of the following power series
(i)
n=0
5n x3n . 2n + 1 (x 1)3n . 3n2 + 2 3n xn .
n=0
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 8.
Due March 12.
8.1. Determine whether the series converges absolutely, conditionally, or diverges. n (i) (1)n1 n + 10
n=1
(ii)
n=1
n5
2 3n 4n + 3
n
(i
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 7.
Due March 5.
7.1. Find the values of p for which the series is convergent: 1 . n(ln n)p n=2 7.2. Determine whether the series converges or diverges. n+
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 6.
Due February 26.
6.1. Determine whether the series
n=1
n2
1 + 5n + 6
is convergent or divergent. If it is convergent, nd its sum. 6.2. Find the value
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 5.
Due February 12.
5.1. Using only the -N denition of convergence of a sequence prove 2n + 1 2 lim =. n 3n + 2 3 5.2. Determine without proof sup S , the
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 3.
Due January 29.
3.1. Evaluate x2
dx 6x + 13 dx 1 e2x
3.2. Evaluate ex 3.3. Evaluate
2x4 + 5 x2 2 dx 2x3 x 1
3.4. Write out the form of the partial fra
CALCULUS 1501 WINTER 2010
HOMEWORK ASSIGNMENT 2.
Due January 22.
2.1. First use a substitution, then integration by parts to evaluate sin(ln x)dx. 2.2. Evaluate
0
ecos t sin 2t dt. 2.3. Use integrati
Philosophy 1230A: Reasoning and Critical Thinking
Rules of Critical Thinking
Description: You are responsible for submitting a list of rules for effective critical thinking that
are inspired by the ma