   Chapter 3.4, Problem 63E

Chapter
Section
Textbook Problem

# Find lim x →   ∞ f ( x ) if 4 x − 1 x < f ( x ) < 4 x 2 + 3 x x 2 for all x > 5 .

To determine

To find:

The limit

limxf(x)

Explanation

1) Concept:

Use Squeeze Theorem to evaluate the limit.

Squeeze Theorem: If f(x)<h(x)<g(x)and limxafx=limxagx=Lthen limxahx=L

2) Given:

4x-1x<fx<4x2+3xx2

3) Calculation:

Here

4x-1x<fx<4x2+3xx2First find

limx4x-1x

=limx4xx-1x

=limx</

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