   Chapter 10, Problem 20RE Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 7–30, calculate the limit algebraically. If the limit does not exist, say why. lim x → 1 / 2 x 2 + 3 x 2 x 2 + 3 x − 1

To determine

To calculate: The value of limx12x2+3x2x2+3x1 algebraically and provide reason if limit does not exist.

Explanation

Given information:

The provided limit is limx12x2+3x2x2+3x1.

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain. If f is a closed form function and f(a) is defined, then limxaf(x) exists and limxaf(x)=f(a).

Calculation:

Consider the limit, limx12x2+3x2x2+3x1

Where, f(x)=x2+3x2x2+3x1

As, f(x)=x2+3x2x2+3x1 is a closed function and its domain does not include x=12, so the limit can be obtained by simplifying the function.

Simplify the function f(x),

f(x)=x2+3x2x2+3x1=x2+3x2x2+4xx1=x2+3x2x(x+2)1(x+2)=x2+3x(2x1)(x+2)

But the function f(x) cannot be simplified further in order to remove the (2x1) term from the denominator

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