4.7 Integration Techniques: Tables
OBJECTIVE: Evaluate integrals using a table of integration formulas.
Table of Integration Formulas
1
dx .
Example 1: Evaluate
4 x2
Math 135
Class Notes Week 11
Bittenger 10th Ed.
1
Example 2: Eva
Math 135 Exam 1 Review Problems and Answers
Bittinger 10th Edition Chapters R, 1, and sections 2.1, 2.2, 2.3
Pages in eText
89
192 193
303
Problem Numbers
9, 10
4 38 all
1 4 all, 7, 11
Answer to Even Problems:
Page 89
10. 3, 25 , x $3 , q 25, 000 units
Pa
Math 135 Business Calculus Written Homework Assignments
Week 2 Due Thursday, 9/5/13
eText Section Problem Numbers
1.1
#35-42 all, 72
Writing Assignment: Write three sentences explaining the
meaning of limit in calculus.
Week 3 Due Thursday, 9/12/13
eText
Math 135 Essay Topic
Due Thursday, 12/5/13
Read pages 469 471 in the text about Lorenz Functions and the Gini Coefficient. (Skip the
part on Regression for Determining Lorenz Functions.)
Write one paragraph in your own words explaining the meaning of bot
1.2 Algebraic Limits and Continuity
OBJECTIVE: Develop and use the Limit Principles to calculate limits. Determine whether a function is
continuous at a point.
Develop an algebraic approach to finding limits.
Limit Properties:
If lim f ( x ) = L
5.7 Differential Equations
OBJECTIVE: Solve differential equations. Verify that a given function is a solution of a
differential equation. Solve differential equations using separation of variables. Solve applications
involving differential equations.
So
5.3 Improper Integrals
OBJECTIVE: Determine whether an improper integral is convergent or divergent. Solve
applied problems involving improper integrals.
Example 1: Find the area of the region under the graph of y =
1
over the interval [1, ) .
x2
Such are
1.6 Differentiation Techniques: The Product and Quotient Rules
OBJECTIVE: Differentiate using the Product and Quotient Rules. Use the Quotient Rule to
differentiate the average cost, revenue, and profit functions.
The Product Rule
THEOREM 5: The Product
3.6 An Economics Application: Elasticity of Demand
OBJECTIVE: Find the elasticity of a demand function. Find the maximum of a totalrevenue function. Characterize demand in terms of elasticity.
Elasticity of Demand is a measure of how sensitive demand is t
2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch
Graphs
OBJECTIVE: Classify the relative extrema of a function using the Second-Derivative Test.
Sketch graphs of continuous functions.
Concavity: Increasing and Decreasing Derivat
2.6 Marginals and Differentials
OBJECTIVE: Find the marginal cost, revenue, and profit. Find y and dy . Use
differentials for approximations.
Mariginal Cost, Revenue, and Profit
The term marginal means rate of change. So, marginal cost is
,
2.5 Maximum-Minimum Problems; Business and Economics Applications
OBJECTIVE: Solve maximum and minimum problems using calculus.
Example 1: Find the maximum profit and the number of units that must be produced and sold in
order to yield the maximum profit