   Chapter 2.6, Problem 33E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the limit or show that it does not exist. lim x → − ∞ ( x 2 + 2 x 7 )

To determine

To show: The value of limx(x2+2x7) does not exist.

Explanation

Theorem used: If r>0 is a rational number, such that xr is defined then limx1xr=0.

Proof:

Consider the function f(x)=x2+2x7.

f(x)=x2+2x7=x7(1x5+2)

Take the limit of f(x) as x approaches negative infinity,

limx(x2+2x7)=limx(x7(1x2+2))=limx(x7)limx(1x2+2)

Note that, the limit law limxaf(x)g(x)=limxaf(x)limxag(x) is valid for one sided limits. That is, if a=±, and also for infinite limits using the rules b×= if b>0

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