   Chapter 9.1, Problem 25E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 15-40, use properties of limits and algebraic methods to find the limits, if they exist. lim x → 10 3 x 2 − 30 x x 2 − 100

To determine

To calculate: The value of the limit limx103x230xx2100.

Explanation

Given Information:

The limit is limx103x230xx2100.

Formula used:

If limxaf(x)=0 and limxag(x)=0, then limxaf(x)g(x) has indeterminate form (00), and factor xa from f(x)andg(x), reduce the fraction and then find the limit of the final expression.

A limit limxax can be simplified as,

limxax=a

The difference of squares can be simplified as,

a2b2=(a+b)(ab)

Calculation:

Consider the provided limit,

limx103x230xx2100

Simplify the limit by substituting 10 for x,

limx103x230xx2100=3(10)

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