BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.5, Problem 2E

(a)

To determine

To find: The graph of y=f(x) intersect vertical and horizontal asymptote.

Expert Solution

Answer to Problem 2E

The graph of y=f(x) cannot intersect vertical asymptote and it may insect horizontal asymptote.

Explanation of Solution

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.5, Problem 2E , additional homework tip  1

From Figure 1, it is clear that the graph of y=f(x) cannot intersect vertical asymptote and it may intersect horizontal asymptote.

(b)

To determine

To find: The possibility number of horizontal asymptotes in the graph.

Expert Solution

Answer to Problem 2E

There are one or two horizontal asymptotes in the graph or no horizontal asymptote also possible.

Explanation of Solution

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.5, Problem 2E , additional homework tip  2

Generally, no horizontal asymptote for polynomial degree one or higher degree.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.5, Problem 2E , additional homework tip  3

Generally, one horizontal for exponential functions.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.5, Problem 2E , additional homework tip  4

Generally, two horizontal asymptotes for inverse tangent functions.

Therefore, horizontal asymptotes exists for limxf(x) and limxf(x).

For the function y=f(x) cannot have more than two horizontal asymptotes.

Thus, from graphs it is observed that there is one or two horizontal asymptote in the graph or no horizontal asymptote also possible.

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