Find the limit. limx →∞ (3 x+5)/(x-4)

Name: Problem 22, Chapter 2: Calculus
Uploaded: 2021-08-24T23:33:35-08:00
Duration: 1 min 36 s
Channel: Carson Merrill
Description: Find the limit. limx →∞ (3 x+5)/(x-4)

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Key Concepts

Limits at Infinity

This concept involves studying the behavior of a function as the independent variable grows without bound. In calculus, limits at infinity help determine the end behavior of functions, particularly in understanding asymptotic behavior and convergence or divergence of functions as they approach infinity.

Rational Functions

A rational function is one that is expressed as the quotient of two polynomials. Evaluating limits involving rational functions often focuses on the highest degree terms since these dominate the behavior of the function as the variable increases or decreases without bound.

Leading Coefficient Comparison

When dealing with limits of rational functions where the degrees of the numerator and denominator are equal, the limit depends on the ratio of their leading coefficients. This simplifies the process of determining the limit, as lower degree terms become negligible compared to the highest degree terms when the variable approaches infinity.

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