Chapter 9, Problem 17RE

### 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

# ssIn Problems 7-20, find each limit, if it exists. 17.   lim x → ∞ f ( x )  where  f ( x ) = { 4 − x 2   if  x < 1 4           if  x = 1 2 x + 1   if  x > 1 .

To determine

To calculate: The value of limx1f(x) for the function, f(x)={4x2   if x<14          if x=12x+1   if x>1.

Explanation

Given Information:

The limit is limxâ†’1f(x) and the provided function is f(x)={4âˆ’x2Â Â Â ifÂ x<14Â Â Â Â Â Â Â Â â€‰Â Â ifÂ x=12x+1Â Â Â â€‰ifÂ x>1.

Formula used:

A limit limxâ†’cx can be simplified as,

limxâ†’cx=c

Calculation:

Consider the provided limit,

limxâ†’1f(x)

The limit from the left is represented by limxâ†’1âˆ’f(x) and the limit from the right is represented by limxâ†’1+f(x).

The limxâ†’cf(x) will exist at c=1 when the limit from the left, that is, the values of f(c) but c<1, is equal to the limit from the right, that is, the values of f(c) but c>1

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