   Chapter 3.4, Problem 53E

Chapter
Section
Textbook Problem

# 52-56 Find the limits as x →   ∞ and as x →   − ∞ . Use this information, together with intercepts, to give a rough sketch of the graph as in Example 11. y = x 4 − x 6

To determine

To find:

The limits as x & x- and draw the graph

Explanation

1) Concept:

Definition of Limit at infinity:

Let f be the function defined on the interval a,  then

limxfx=L

Means that for every positive number M there is a corresponding positive N such that

If x>N  then fx>M

2) Given:

y=x4-x6

3) Calculation:

Consider the given function,

y=x4-x6

To find the limit as x,

limxy=limxx4-x6

=limxx4(1-x2)

Apply limit separately,

=limxx4·limx1-x2

=·-

=-

Now, find the limit as x-,

limx-y=limx-x4-x6

=limx-x4

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