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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

Each of Problems 21-24 contains a function and its graph. For each problem, answer parts (a) and (b).

(a) Use the graph to determine, as well as you can,

(i) vertical asymptotes, (ii) lim lim x   f ( x ) .

(iii) lim x       f ( x )

. (iv) horizontal asymptotes.

(b) Check your conclusions in (a) by using the functions to determine items (i)-(iv) analytically.

f ( x ) = 4 x 2 x 2 4 x + 4

Chapter 9.2, Problem 24E, Each of Problems 21-24 contains a function and its graph. For each problem, answer parts (a) and

(a)

To determine

The vertical asymptote of the function f(x)=4x2x24x+4, limxf(x), limxf(x) and horizontal asymptotes using the graph of the function,

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 9.2, Problem 24E , additional homework tip  1

Explanation

Given Information:

The function is f(x)=4x2x24x+4. The graph for the function is

Explanation:

Consider the provided function,

f(x)=4x2x24x+4

Consider the provided graph of the function,

The vertical asymptote is the line, which is approached by the graph of the function, but never really intersects or touches it.

In the provided graph, the line x=2 is the line which is approached by the graph of the function, but never really intersects or touches it.

Hence, the vertical asymptote of the function is x=2.

Consider the provided limit,

limxf(x)

At x=, the graph of the function approaches the x-axis, that is, the value of the function approaches 4

(b)

To determine

Whether the vertical asymptote of the function f(x)=4x2x24x+4, limxf(x), limxf(x) and horizontal asymptotes calculated using the graph of the function is correct or not,

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 9.2, Problem 24E , additional homework tip  2

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