Math 104 - Calculus II - Reading Assignments March 1999 Be sure to check back, because this may change during the semester. (Last modified: Sunday, March 7, 1999, 10:44 PM ) I'll use Maple syntax for mathematical notation on this page. All numbers indicate sections from Ostebee/Zorn, Vol 2. For March 1 Section 8.1 Introduction to Using the Definite Integral Section 8.2 Finding Volumes by Integration To read : All Be sure to understand : The section from 8.2 on Reassembling Riemann's Loaf and Example 1 from 8.2. Email Subject Line : Math 104 3/1 Your Name Reading Questions : Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis? Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis? For March 3 Sick Day today. No class. For March 5 Section 8.2 Finding Volumes by Integration To read : Re-read the section for today Be sure to understand : Example 3 Email Subject Line : Math 104 3/3 Your Name Reading Questions: Consider the region R bounded by the graphs y=x and y=x2. (Notice R is in the first quadrant). Set up the integral that gives the volume of the solid formed when R is rotated about the x-axis the y-axis For March 8 Section 8.3 Arclength To read : All Be sure to understand : The statement of the Fact at the bottom of page 468, and Example 2. Email Subject Line : Math 104 3/8 Your Name Reading Question : Use the Fact on page 468 to set up the integral that gives the length of the curve y=x3 from x=1 to x=3. For March 10 Section 10.1 When Is an Integral Improper? To read : All Be sure to understand : Examples 1, 2, and 4. The formal definitions of convergence and divergence on pages 523 and 524. Email Subject Line : Math 104 3/10 Your Name Reading Questions : What are the two ways in which an integral may be improper? Explain why int( 1/x2, x=1..infty) is improper. Does the integral converge or diverge? Explain why int( 1/x2, x=0..1) is improper. Does the integral converge or diverge? For March 12 Section 10.2 Detecting Convergence, Estimating Limits To read : All Be sure to understand : Example 2 and the statement of Theorem 1 Email Subject Line : Math 104 3/12 Your Name Reading Questions : If 0 < f(x) < g(x) and int( g(x), x=1. . infty) converges, will int(f(x), x=1. .infty) converge or diverge? Why? There are two types of errors that arise in Example 2 for approximating int( 1/(x5 +1), x=1..infty). What are the two types? March 15 - 19 Spring Break. For March 22 Work on Project 2 today. No Reading Assignment. For March 24 Section 10.3 Improper Integrals and Probability To read : All Be sure to understand : The section The Normal Density Function Email Subject Line : Math 104 3/24 Your Name Reading Questions : What is a probability density function? What is the connection between a probability density function and integration? For March 26 Section 10.4 l'Hopital's Rule: Comparing Rates To read : All, but you may skip the section on Fine Print: Pointers Toward a Proof. We'll talk about a different justification during class. Be sure to understand : The statement of Theorem 3, l'Hopital's Rule. Email Subject Line : Math 104 3/26 Your Name Reading Questions : Does l'Hopital's Rule apply to lim(x -> infty) x2 / ex ? Why or why not? Does l'Hopital's Rule apply to lim(x -> infty) x2 / sin(x) ? Why or why not? For March 29 The Big Picture. No reading assignment for today. For March 31 Section 11.1 Sequences and Their Limits To read : Through page 557 and the statements of Theorem 2 and Theorem 3. Be sure to understand : The section of Fine Points on page 553, the statements of Theorems 2 and 3. Email Subject Line : Math 104 3/31 Your Name Reading Questions : Does the following sequence converge or diverge? Be sure to explain your answer. 1, 3, 5, 7, 9, 11, 13, . . . Find a symbolic expression for the general term ak of the sequence 1, -2, 4, -8, 16, -32, . . . Math 104 Home | T. Ratliff's Home