5 THE INTEGRAL
5.1 Approximating and Computing Area
Preliminary Questions
If the interval [2, 5] is divided into six subintervals, the length of each subinterval is 52 = 1 . The right 6 2 endpoints of the subintervals are then 5 , 3, 7 , 4, 9 , 5, while t
APPLICAT IONS OF 6 THE INTEGRAL
6.1 Area Between Two Curves
Preliminary Questions
b
1. What is the area interpretation of
SOLUTION
of y = f (x ) and y = g (x ), bounded on the left by the vertical line x = a and on the right by the vertical line x = b.
b
5 THE INTEGRAL
5.1 Approximating and Computing Area
Preliminary Questions
If the interval [2, 5] is divided into six subintervals, the length of each subinterval is 52 = 1 . The right 6 2 endpoints of the subintervals are then 5 , 3, 7 , 4, 9 , 5, while t
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MAT 1 15 {estructorz Mike Wang
NAME:
Sample Midterm
Show a}? year work eieariy! If you finish eaﬁy, don’t fergei to check your work.
1. Answer the foilowing: (20 pts) (2 pts each)
* (True or False): Iffis coniinuous on (a, b], then there exists a number {
Math 115
January 23, 2016
Review Sheet
Exam 1 is Thursday, January 28, and will cover chapter 5, sections 1 to 5 and chapter 6,
sections 1 & 2. The following is a list of the topics which you may expect to appear on the
exam:
1. Computing definite integra
Math 115
March 7, 2016
Final Review Sheet
A comprehensive final exam will be given on Thursday, March 17th, Section 8 - 9:10 11:10, Section 10 - 11:30 1:30.
The exam is comprehensive and will cover chapter 5,chapter 6, sections 1 to 7, chapter
7, sections
TECHNIQUES OF 7 INTEGRATION
7.1 Numerical Integration
Preliminary Questions
1. What are T1 and T2 for a function on [0, 2] such that f (0) = 3, f (1) = 4, and f (2) = 3?
SOLUTION
Using the given function values T1 = 1 (2)(3 + 3) = 6 and 2 T2 = 1 (1)(3 + 8
Table of Contents
Preliminaries
2.1 Velocities and Tangents
2.2 The Limit of a Function
2.3 Calculating Limits Using Limit Laws
2.4 The Precise Definition of Limit.
2.5 Continuity
2.6 Limits at infinity.
2.7 The Derivatives and Rates of Change
2.8, 3.1 T
Syllabus for Math 115Calculus & Analytic Geometry
Cal Poly Pomona
Spring 2012
Instructor: Bill Edwards Phone: 869-4010 E-mail: [email protected]
Text: Single Variable Calculus: ET California Edition with Classics 6ed
115-06 Course Ref. #31396 T,Th 10
Math 115
February 18, 2016
Review Sheet
Exam 2 is Thursday, February 25, and will cover chapter 6, sections 2 - 4 and chapter 7
sections 1 - 5 as discussed in lecture. We have covered:
a) Area between curves
b) Volumes of solids of revolution
c) Integrati