   Chapter 10.5, Problem 1E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-4, a function and its graph are given. Use the graph to find each of the following, if they exist. Then confirm your results analytically.(a) vertical asymptotes (b) lim x → ∞ f ( x ) (c) lim x → − ∞ f ( x ) (d) horizontal asymptotes f ( x ) = x − 4 x − 2 (a)

To determine

The vertical asymptote of the function f(x)=x4x2 from the provided graph, Also, verify the result analytically.

Explanation

Given Information:

The provided graph of the function f(x)=x4x2 is

.

Explanation:

A vertical asymptote of a function f(x) is a line x=a such that f(a)=.

A vertical asymptote of a rational function h(x)=f(x)g(x) is x=a where g(a)=0 and f(a)0.

Consider the provided graph,

At x=2 the graph of the function increases indefinitely.

Thus, the vertical asymptote is the line x=2.

Now, consider the function f(x)=x4x2

(b)

To determine

The value of limxf(x) for a function f(x)=x4x2 from the provided graph, Also, verify the result analytically.

(c)

To determine

The value of limxf(x) for a function f(x)=x4x2 from the provided graph of Also, verify the result analytically.

(d)

To determine

The horizontal asymptote of the function f(x)=x4x2 from the provided graph, Also, verify the result analytically.

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