step 1 Welcome. We're going to take the limit as x approaches negative 2 of x cubed minus x plus 5. So

Question

$$\lim _{x \rightarrow-2}\left(x^{3}-x+5\right)$$

Name: Problem 4, Chapter 10: Precalculus: Graphical, Numerical, Algebraic
Uploaded: 2020-03-02T03:17:16-08:00
Duration: 38 s
Channel: Aditya Sood
Description: limx →-2(x^3-x+5)

   $$\lim _{x \rightarrow-2}\left(x^{3}-x+5\right)$$

Precalculus: Graphical, Numerical, Algebraic

Franklin D.… 8th Edition

Chapter 10, Problem 4

Instant Answer

Solved by Expert Aditya Sood

03/02/2020

Step 1

The first step in solving limits is to substitute the given value of x into the function. Show more…

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$$\lim _{x \rightarrow-2}\left(x^{3}-x+5\right)$$

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Key Concepts

Limit of a Function

This concept involves evaluating the value that a function approaches as the input approaches a particular point. It is a fundamental idea in calculus that helps in understanding the behavior of functions near specific values, even if the function is not defined at that point.

Direct Substitution Method

When evaluating limits, if the function is continuous at the point of interest, one can substitute the value directly into the function to find the limit. This method simplifies the process by utilizing the inherent properties of continuous functions.

Continuity of Polynomial Functions

Polynomial functions are continuous across all real numbers, meaning they have no breaks, jumps, or holes. This property assures that using direct substitution to evaluate the limit at any point is valid, as the function’s behavior is predictable and well-defined.

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