Important Terms and Concepts
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Learning OutcomesIn this chapter, students will...
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Chapter 6 Sections
6-2 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 1-10, 1-25 odd
Videos of selected problems: #1
Homework - Day 2: Problems 27-59 odd, 60-63 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 1-10, 1-25 odd
Videos of selected problems: #1
Homework - Day 2: Problems 27-59 odd, 60-63 all
6-3 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 1-10, 1-13 odd
Homework - Day 2: Problems 15-29 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 1-10, 1-13 odd
Homework - Day 2: Problems 15-29 odd, 30
6-4 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 1-10, 1-15 odd
Homework - Day 2: Problems 2, 4, 6, 17-33 odd
Homework - Day 3: Problems 35-63 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 1-10, 1-15 odd
Homework - Day 2: Problems 2, 4, 6, 17-33 odd
Homework - Day 3: Problems 35-63 odd
6-5 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 1-10, 1-21 odd
Homework - Day 2: Problems 23-35 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 1-10, 1-21 odd
Homework - Day 2: Problems 23-35 odd, 36
Aligned Instructional Resources: Khan Academy Video
6-6 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 1-30 all
Homework - Day 2: Problems 31-60 all
Homework - Day 3: Problems 61-90 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 1-30 all
Homework - Day 2: Problems 31-60 all
Homework - Day 3: Problems 61-90 all
