Question

Find the limit. $$ \lim _{x \rightarrow-2}(3 x-1) $$

   Find the limit.
$$
\lim _{x \rightarrow-2}(3 x-1)
$$

Calculus

Earl W. Swokowski 5th Edition

Chapter 2, Problem 1

Instant Answer

Solved by Expert Nick Johnson

03/01/2022

Step 1

Step 1: We are given the function $f(x) = 3x - 1$ and we are asked to find the limit as $x$ approaches $-2$. Show more…

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Find the limit. $$ \lim _{x \rightarrow-2}(3 x-1) $$

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Key Concepts

Limit of a Function

The limit of a function is a fundamental concept in calculus that describes the behavior of the function's output as its input tends to a particular value. It is used to understand how functions behave near points of interest, even if the function might not be defined at that point.

Continuity

Continuity is a property of a function indicating that small changes in the input produce small changes in the output, and the function is unbroken and smooth at a point. For a continuous function, the limit as the input approaches a specific value is the same as the function's value at that point.

Direct Substitution

Direct substitution is a straightforward technique for evaluating limits by plugging the value that the variable approaches directly into the function. This method works when the function is known to be continuous at that point, allowing one to bypass more complex algebraic manipulations.

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