# The lim x → 0 tan 3 x tan 5 x . Also confirm the result graphically.

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 2.2, Problem 22E
To determine

## To calculate: The limx→0tan3xtan5x . Also confirm the result graphically.

Expert Solution

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,

Therefore, limx0tan3xtan5x=35

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