   Chapter 2.6, Problem 26E ### 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 + 3 x 2 4 x − 1

To determine

To show: The value of limxx+3x24x1 does not exists.

Explanation

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

Proof:

Consider f(x)=x+3x24x1.

Divide both the numerator and the denominator by the highest power of x in the denominator. That is, x0.

f(x)=x+3x2x4x1x =xx+3x2x4xx1x=1+3x41x

Take the limit of f(x) as x approaches infinity.

limxx+3x24x1=limx1+3x41x

As x goes to infinity, 1+3x goes to infinity. That is, limx(1+3x)=.

As x goes to infinity, 41x goes to 4

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