BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.2, Problem 22E
To determine

To calculate: The limx0tan3xtan5x . Also confirm the result graphically.

Expert Solution

Answer to Problem 22E

  limx0tan3xtan5x=35 .

Explanation of Solution

Given information:

Given limit as limx0tan3xtan5x

Consider the limits as, limx0tan3xtan5x

Since, tanx=x+13x3+215x5+...

Hence, limx0tan3xtan5x=limx0(3x)+13(3x)3+215(3x)5+...(5x)+13(5x)3+215(5x)5+...

Then,

  limx0tan3xtan5x=limx03x+9x3+1625x5+...5x+1253x3+12503x5+...=limx0x(3+9x2+1625x4+...)x(5+1253x2+12503x4+...)=limx03+9x2+1625x4+...5+1253x2+12503x4+...=3+0+0+...5+0+0+...=35=0.6

Graph of the function is,

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 22E

Therefore, limx0tan3xtan5x=35

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