Education Technology

Natural Logarithm

Updated on 07/01/2014

Activity Overview

Construct the graph of the natural logarithm function from its definition.

Objectives

  • Understand the definition of the natural logarithm function in terms of a definite integral
  • Use this definition to relate the value of the natural logarithm function to the area under a curve
  • Use the Fundamental Theorem of Calculus to compute the derivative of the natural logarithm function
  • Use the derivative of the natural logarithm (1/x) to determine properties of its graph

Vocabulary

  • natural logarithm function
  • area under a curve
  • increases without bound
  • derivative
  • Fundamental Theorem of Calculus

About the Lesson

This lesson involves constructing the graph of the natural logarithm function from its definition. As a result, students will:

  • Conjecture about the value of the natural logarithm function as x increases without bound.
  • Conjecture about the value of the natural logarithm function as x approaches 0 from the right.
  • Use the derivative to discover properties of the graph of the natural logarithm function.