   Chapter 3.4, Problem 52E

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 = 2 x 3 − x 4 .

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 some 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=2x3-x4

3) Calculation:

Consider the given function,

y=2x3-x4

To find the limit as x,

limxy=limx2x3-x4

=limxx3(2-x)

Apply limit separately,

=limxx3·limx2-x

=·-

=-

Now, find the limit as x-,

limx-y=limx-2x3

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