Question

Evaluate $\lim _{x \rightarrow \infty}$ for the function. $$f(x)=\frac{x^{2}+4}{x+3}$$

Name: Problem 47, Chapter 1: Calculus Single Variable
Uploaded: 2021-04-28T21:38:54-08:00
Duration: 53 s
Channel: Prashansha Kaushik
Description: Evaluate limx →∞ for the function. f(x)=(x^2+4)/(x+3)

   Evaluate $\lim _{x \rightarrow \infty}$ for the function.
$$f(x)=\frac{x^{2}+4}{x+3}$$

Calculus Single Variable

Deborah… 7th Edition

Chapter 1, Problem 47

Instant Answer

Solved by Expert Prashansha Kaushik

04/28/2021

Step 1

We get: $$f(x)=\lim _{x \rightarrow \infty} \frac{x(x+4/x)}{x(1+3/x)}$$ Show more…

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Evaluate $\lim _{x \rightarrow \infty}$ for the function. $$f(x)=\frac{x^{2}+4}{x+3}$$

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Key Concepts

Dominant Term Analysis

When evaluating the limit at infinity of a rational function, the highest degree terms in the numerator and denominator dominate the behavior of the function. Focusing on these dominant terms simplifies the process, allowing one to approximate the limit without the lower-degree terms affecting the outcome.

Rational Functions

Rational functions are expressions formed by the ratio of two polynomials. Analyzing such functions, especially for limits at infinity, often requires comparing the degrees of the numerator and the denominator.

Limit

The concept of limits involves evaluating the behavior of a function as it approaches a particular point, or as the variable tends towards infinity. This is fundamental in calculus for understanding the asymptotic behavior and continuity of functions.

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