   Chapter 3.4, Problem 28E

Chapter
Section
Textbook Problem

# 9-32 Find the limit or show that it does not exist. lim x →   − ∞ 1 + x 6 x 4 + 1

To determine

To find:

lim- ∞1+x6x4+1

Explanation

1) Concept:

To evaluate the limit at infinity of any rational function, first divide both the numerator and denominator by the highest power of x that occurs in the denominator.

2) Formula:

i) Sum law: lim[px+qx]=limp(x)+limq(x)

ii) Quotient law:limpxqx=limp(x)limq(x)

3) Given:

lim -1+x6x4+1

4) Calculation:

Here, highest power of denominator is 4, divide numerator and denominator by x4

lim -1+x6x4+1=lim- ∞1+x6x4x4+1x4

= lim- ∞1x4+x6x4x4x4+1x4

=lim- ∞1x4+x21+1x4

By using quotient law of limit

= lim(x - 1x4+x2) limx  -(1+1x4)

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