Chapter 9.1, Problem 27E

### 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 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 limxâ†’103x2âˆ’30xx2âˆ’100.

Formula used:

If limxâ†’af(x)=0 and limxâ†’ag(x)=0, then limxâ†’af(x)g(x) has indeterminate form (00), and factor xâˆ’a from f(x)andg(x), reduce the fraction and then find the limit of the final expression.

A limit limxâ†’ax can be simplified as,

limxâ†’ax=a

The difference of squares can be simplified as,

a2âˆ’b2=(a+b)(aâˆ’b)

Calculation:

Consider the provided limit,

limxâ†’103x2âˆ’30xx2âˆ’100

Simplify the limit by substituting 10 for x,

limxâ†’103x2âˆ’30xx2âˆ’100=3(10)

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