   Chapter 9.1, Problem 6CP ### 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

# Evaluate the following limits (if they exist).(a) lim x → − 3 2 x 2 + 5 x − 3 x 2 − 9 (b) lim x → 5 x 2 − 3 x − 3 x 2 − 8 x + 1 (c) lim x → − 3 / 4 4 x 4 x + 3

(a)

To determine

To calculate: The value of the limit, limx32x2+5x3x29.

Explanation

Given Information:

The limit, limx32x2+5x3x29.

Formula used:

If limxcf(x)=0 and limxcg(x)=0, then limxcf(x)g(x) has 00 indeterminate form at x=c. To find the limit, firstly factor xc from f(x)andg(x) then divide out the common factor and reduce the fraction.

Calculation:

Consider the provided limit,

limx32x2+5x3x29

Simplify the limit by substituting 3 for x,

limx32x2+5x3x29=2(3)2+5(3)3(3)29=2(9)15399=18180=00

Since, the limit has 00 indeterminate form at x=c

(b)

To determine

To calculate: The value of the limit, limx5x23x3x28x+1.

(c)

To determine

To calculate: The value of the limit, limx344x4x+3.

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