Chapter 9, Problem 19RE

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 7-20, find each limit, if it exists. lim h → 0 3 ( x + h ) 2 − 3 x 2 h

To determine

To calculate: The value of the limit limh03(x+h)23x2h.

Explanation

Given Information:

The provided limit is limhâ†’03(x+h)2âˆ’3x2h.

Formula used:

A limit limxâ†’cx can be simplified as,

limxâ†’cx=c

The property of square of sum of two terms a and b states that,

(a+b)2=a2+b2+2ab

Calculation:

Consider the provided limit,

limhâ†’03(x+h)2âˆ’3x2h

Rewrite the limit using the property of square of sum of two terms,

limhâ†’03(x+h)2âˆ’3x2h=limhâ†’03(x2+h2+2xh)âˆ’3x2h

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