   Chapter 9.1, Problem 39E Mathematical Applications for the ...

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

Solutions

Chapter
Section Mathematical Applications for the ...

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

In Problems 15-40, use properties of limits and algebraic methods to find the limits, if they exist. lim h → 0 ( x + h ) 3 − x 3 h

To determine

To calculate: The value of the limit limh0(x+h)3x3h.

Explanation

Given Information:

The limit is limh0(x+h)3x3h.

Formula used:

A limit limxcx can be simplified as,

limxcx=c

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

(a+b)3=a3+b3+3a2b+3ab2

Calculation:

Consider the provided limit,

limh0(x+h)3x3h

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

limh0(x+h)3x3h=limh0x3+h3+3x2h+3xh2x3h=limh

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