   Chapter 2.3, Problem 2E ### 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

# Tire graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does not exist, explain why.(a) lim x → 2 [ f ( x ) + g ( x ) ] (b) lim x → 0 [ f ( x ) − g ( x ) ] (c) lim x → − 1 [ f ( x ) g ( x ) ] (d) lim x → 3 f ( x ) g ( x ) (e) lim x → 2 [ x 2 f ( x ) ] (f) f ( − 1 ) + lim x → − 1 g ( x ) (a)

To determine

To evaluate: The value of limx2[f(x)+g(x)].

Explanation

Limit Laws:

Suppose that c is a constant and the limits limxaf(x) and limxag(x) exist. 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 9: limxaxn=an where n is a positive integer

(b)

To determine

To evaluate: The value of limx0[f(x)g(x)].

(c)

To determine

To evaluate The value of limx1[f(x)g(x)].

(d)

To determine

To evaluate: The value of limx3[f(x)g(x)].

(e)

To determine

To evaluate: The value of limx2[x2f(x)].

(f)

To determine

To evaluate: The value of f(1)+limx1g(x).

### 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

#### f(x)=1x2+1; limxf(x); and limxf(x) x 1 10 100 1000 f(x) x 1 10 100 1000 f(x)

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

#### 43. What is the domain of Check with a graphing utility.

Mathematical Applications for the Management, Life, and Social Sciences

#### The slope of the tangent line to r = cos θ at is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### What is the goal of a single-case experimental research design?

Research Methods for the Behavioral Sciences (MindTap Course List) 