   Chapter 2.6, Problem 17E

Chapter
Section
Textbook Problem

Find the limit or show that it does not exist. lim x → − ∞ x − 2 x 2 + 1

To determine

To find: The value of limxx2x2+1.

Explanation

Limit Laws used: Suppose that c is a constant and the limits limxaf(x) and limxag(x) exists, then

Limit law 1: limxa[f(x)+g(x)]=limxaf(x)+limxag(x)

Limit law 2: limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 3: limxa[cf(x)]=climxaf(x)

Limit law 4: limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 5: limxaf(x)g(x)=limxaf(x)limxag(x) if limxag(x)0

Limit law 6: limxa[f(x)]n=[limxaf(x)]n where n is a positive integer.

Limit law 7: limxac=c

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

Calculation:

Obtain the value of the function as x approaches negative infinity.

Consider f(x)=x2x2+1.

Divide both the numerator and the denominator by the highest power of x in the denominator. That is, x20.

f(x)=x2x2x2+1x2=xx22x2x2x2+1x2=1x2x21+1x2

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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 914, evaluate the expression. 14. 3543183

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Differentiate the function. y = log2 (x log5 x)

Single Variable Calculus: Early Transcendentals, Volume I

Fill in each blank: 3tbs=tsp

Elementary Technical Mathematics

Show that if z=cos+isin, then | z |=1.

Trigonometry (MindTap Course List) 