Question

Find the limit. $\lim _{x \rightarrow-1} \frac{4 x-5}{3-x}$

   Find the limit.
$\lim _{x \rightarrow-1} \frac{4 x-5}{3-x}$

Calculus an Applied Approach

Calculus an Applied Approach

Ron Larson, David C,… 8th Edition

Chapter 1, Problem 34

Instant Answer

Solved by Expert Kim Matthews

06/13/2021

Step 1

In this case, the denominator of the function is $3 - x$. If we substitute $x = -1$, we get $3 - (-1) = 4$, which is not zero. Therefore, we can directly substitute $x = -1$ into the function. Show more…

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Find the limit. $\lim _{x \rightarrow-1} \frac{4 x-5}{3-x}$

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Key Concepts

Rational Functions

Rational functions are expressions formed by the ratio of two polynomials. Evaluating limits involving rational functions often involves checking for continuity and applying direct substitution unless the substitution results in an indeterminate form, in which case additional algebraic techniques are required.

Limit

The concept of a limit describes the behavior of a function as the input variable approaches a specific value. It is a foundational idea in calculus used to understand the behavior of functions in cases where the function might not be explicitly defined at that point.

Direct Substitution

Direct substitution is a technique used to evaluate limits by plugging the point of interest directly into the function. This method works well when the function is continuous at the point, meaning that the limit exists and is equal to the function's value at that point.

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