Chapter 8.7, Problem 9E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

# Using Two Methods In Exercises 5–10, evaluate the limit (a) using techniques from Chapters 1 and 3 and (b) using L’Hôpital’s Rule. lim x → ∞ 5 x 2 − 3 x + 1 3 x 2 − 5

(a)

To determine

To calculate: The value of limit limx5x23x+13x25.

Explanation

Given:

The provided function is limx5x23x+13x25.

Formula used:

Property of rational functions:

In a limit, if the degree of the numerator is equal to the degree of the denominator, then the limit of the rational function is the ratio of the leading coefficients.

Calculation:

Consider the function 5x23x+13x25.

Degree of numerator is 2 and the degree of denominator is also 2.

The provided function 5x23x+13x25 is a rational function in which the degree of numerator is equal to the degree of denominator, so the property of rational functions is applicable.

Recall the property of rational functions:

In a limit if the degree of the numerator is equal to degree of denominator, then the limit of the rational function is the ratio of the leading coefficients

(b)

To determine

To calculate: The value of limit limx5x23x+13x25 by the use of L’Hospital’s rule.

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