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Math 12003--002
Analytic Geometry and Calculus II
Fall 2003

Exercise Set 4

Date Due Required Kicker (optional) Collected?*
Section Exercises Section Exercises
Monday, 10/20/03 No assignment!
Tuesday, 10/21/03 Class Notes For each of the three functions:
  1. f(x)=ln(1+x)
  2. f(x)=sin(x)
  3. f(x)=cos(x)
  • Sketch and compute the Taylor polynomials T_0(x),T_1(x), and T_2(x).
  • Compute T_3(x) and T_4(x).
Class Notes For the three functions given, find the nth Taylor polynomial T_n(x) Yes- HW 11
Wednesday, 10/22/03 Lectures on Power Series:
"Taylor Polynomials" 		Assignment at bottom of page, all functions except y=ln(1+kx) and y=sin(x). Lectures on Power Series:
"Taylor Polynomials" 		Assignment at bottom of page for the function y=ln(1+kx). Yes- HW 12
Thursday, 10/23/03 Lectures on Power Series:
"Taylor Polynomials" 		Find the nth Taylor polynomial T_n(x), in sigma notation, for the functions:
  1. f(x) = 1 / (1-x)
  2. f(x) = 1 / (1-3x)
  3. f(x) = 1 / (1-kx), where k is a nonzero real number
Lectures on Power Series: Find the 5th Taylor polynomial for f(x) = arctan x No
Friday, 10/24/03 4.2 1-7 odd; 8; 11-15 odd 4.2 14, 16 No
Quiz 10 covers Taylor polynomials.
Monday, 10/27/03 Class canceled due to illness. Sorry for any inconvenience.
Tuesday, 10/28/03 4.2 6, 26, 28, 32, 33 4.2 34 Yes- HW 13
Wednesday, 10/29/03 Lectures on Power Series:
Taylor's Theorem		 Read the notes. We will go over the examples in class tomorrow.
Thursday, 10/30/03 Lectures on Power Series:
Taylor's Theorem		 For each function f and value b, find the values of the 0th through 4th Taylor polynomials as well as the limit as n approaches infinity of the remainder after n terms.
  1. f(x)= e^x; b=2, b= - 1
  2. f(x)= ln(1+x); b=2, b= - 1/3
  3. f(x)= sin x; b=pi/2,
Lectures on Power Series:
Taylor's Theorem		 f(x)= sin x; b= - pi No
Friday, 10/31/03 Lectures on Power Series:
Taylor's Theorem		 For the function f(x)= cos x and value b given below, find the values of the 0th, 2nd, 4th, through 20th Taylor polynomials.
  1. b=pi/2,
  2. b= - pi/2,
  3. b=pi,
  4. b= - 5pi,
Lectures on Power Series:
Taylor's Theorem		 Determine if the remainder approaches 0 for each b in the previous exercise. No
Quiz will be Monday.
Monday, 11/3/03 Lectures on Power Series:
Radius of Convergence of a Power Series		 read the notes 12.8 Find the radius of convergence only for:
27 		No
12.8 Find the radius of convergence only for:
3, 4, 5, 6, 9, 11, 28
Quiz 11 covers Taylor's Theorem (Taylor polynomials and their remainders).
Tuesday, 11/4/03 Lectures on Power Series:
Differentiation		 Problems from the board.
(Sorry, too hard to type in html.)		 Lectures on Power Series:
Differentiation		 Problem from the board. No
Wednesday, 11/5/03 Lectures on Power Series:
Integration		 Integrate each of the functions from last night's homework. Lectures on Power Series:
Integration		 Same. No
Thursday, 11/6/03 12.10 5, 22, 24, 25, 31 12.10 33 No
Friday, 11/7/03 Lectures on Power Series: exercises from the board Lectures on Power Series: from the board Yes- HW 14
Quiz 9
Monday, 11/10/03 Exam 4

Next Exercise Set

* I will roll the dice twice daily in each class to determine if that day's assignment will be collected in that class. I will collect on doubles, 7, or 11. (Rules may change as the semester progresses to insure that I collect 20 assignments.) Each assignment is worth 5 points plus 1 possible bonus point. (The bonus point will be given for the completion of the optional "kicker" problems.) You must show your work; no credit will be given for homework that gives just the answers. Homework turned in late (for any reason) will receive at most 3 out of the 5 possible points (and no credit for the kicker). Homework may be turned in early to me or my mailbox for full credit. No homework will be accepted after 5:00 pm on December 5, 2003.

Darci L. Kracht
dkracht@kent.edu