Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Fundamental Theorem

9-12

45 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.6

## Natural Logarithm

#### 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.