   Chapter 3.4, Problem 1E

Chapter
Section
Textbook Problem

# Explain in your own words the meaning of each of the following.(a) lim x → ∞ f ( x ) = 5 (b) lim x → − ∞ f ( x ) = 3

To determine

(a)

To explain:

The meaning of limxf(x)=5

Explanation

1) Concept:

Use definition of limit at infinity

2) Definition

Limit at infinity: Let f be function defined on (a,). Then

limxf(x)=L

Means that the values of f(x) can be made arbitrarily close to L by requiring x to be sufficiently large. (means values of f(x) approaches L as x becomes larger and larger

To determine

(b)

To explain:

The meaning of limx-f(x)=3

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