Important Terms and Concepts

Learning OutcomesIn this chapter, students will...

Chapter 6 Sections
62 Antiderivative of the Reciprocal Function, and Another Form of the Fundamental Theorem
Objective: Find out how to differentiate a function defined as a definite integral between a fixed lower limit and a variable upper limit, and use the technique to integrate the reciprocal function.
Homework  Day 1: Q Problems 110, 125 odd
Videos of selected problems: #1
Homework  Day 2: Problems 2759 odd, 6063 all
Objective: Find out how to differentiate a function defined as a definite integral between a fixed lower limit and a variable upper limit, and use the technique to integrate the reciprocal function.
Homework  Day 1: Q Problems 110, 125 odd
Videos of selected problems: #1
Homework  Day 2: Problems 2759 odd, 6063 all
63 The Uniqueness Theorem and Properties of Logarithmic Functions
Objective: Learn the uniqueness theorem for derivatives, and use it to prove that ln x, defined as an integral, is a logarithmic function and has the properties of logarithms. Use these properties to differentiate logarithmic functions with any acceptable base.
Homework  Day 1: Q Problems 110, 113 odd
Homework  Day 2: Problems 1529 odd, 30
Objective: Learn the uniqueness theorem for derivatives, and use it to prove that ln x, defined as an integral, is a logarithmic function and has the properties of logarithms. Use these properties to differentiate logarithmic functions with any acceptable base.
Homework  Day 1: Q Problems 110, 113 odd
Homework  Day 2: Problems 1529 odd, 30
64 The Number e, Exponential Functions, and Logarithmic Differentiation
Objective: Derive properties of y=e^x starting with its definition as the inverse of y=ln x. Use the results to define b^x, and differentiate exponential functions by first taking the natural logarithm.
Homework  Day 1: Q Problems 110, 115 odd
Homework  Day 2: Problems 2, 4, 6, 1733 odd
Homework  Day 3: Problems 3563 odd
Objective: Derive properties of y=e^x starting with its definition as the inverse of y=ln x. Use the results to define b^x, and differentiate exponential functions by first taking the natural logarithm.
Homework  Day 1: Q Problems 110, 115 odd
Homework  Day 2: Problems 2, 4, 6, 1733 odd
Homework  Day 3: Problems 3563 odd
65 Limits of Indeterminate Forms  l'Hospital's Rule
Objective: Given an expression with an indeterminate form, find its limit using l'Hospital's rule..
Homework  Day 1: Q Problems 110, 121 odd
Homework  Day 2: Problems 2335 odd, 36
Aligned Instructional Resources: Khan Academy Video
Objective: Given an expression with an indeterminate form, find its limit using l'Hospital's rule..
Homework  Day 1: Q Problems 110, 121 odd
Homework  Day 2: Problems 2335 odd, 36
Aligned Instructional Resources: Khan Academy Video
66 Derivative and Integral Practice for Transcendental Functions
Objective: Be able to differentiate and integral algebraically functions involving logs and exponentials quickly and correctly so that you can concentrate on the applications in he following chapters.
Homework  Day 1: Problems 130 all
Homework  Day 2: Problems 3160 all
Homework  Day 3: Problems 6190 all
Objective: Be able to differentiate and integral algebraically functions involving logs and exponentials quickly and correctly so that you can concentrate on the applications in he following chapters.
Homework  Day 1: Problems 130 all
Homework  Day 2: Problems 3160 all
Homework  Day 3: Problems 6190 all