Chapter 4.5, Problem 11E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Finding Limits at Infinity In Exercises 11 and12, find lim x → ∞ h ( x ) , if it exists. f ( x ) = 5 x 3 − 3 (a) h ( x ) = f ( x ) x 2 (b) h ( x ) = f ( x ) x 3 (c) h ( x ) = f ( x ) x 4

(a)

To determine

To calculate: The specified limit for the function f(x)=5x33 and h(x)=f(x)x2 at infinity if it exists.

Explanation

Given:

The functions f(x)=5x3âˆ’3 and h(x)=f(x)x2.

Formula Used:

The limit of a rational function at infinity could be computed as follows:

If the power of the first terms of the numerator is greater than the power of the first term of the denominator, the limit of the provided rational function at infinity would not exist.

If the power of the first terms of the numerator is less than the power of the first term of the denominator, the limit of the provided rational function at infinity would be zero.

If the power of the first terms of the numerator is equal to the power of the first term of the denominator, the limit of the provided rational function at infinity would be ratio of the coefficient of the first term in the numerator and the coefficient of the first term in the denominator

(b)

To determine

To calculate: The specified limit for the function f(x)=5x33 and h(x)=f(x)x3 at infinity if it exists.

(c)

To determine

To calculate: The specified limit for the function f(x)=5x33 and h(x)=f(x)x4 at infinity if it exists.

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