/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 Find the limit. $$ \lim _{x ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 24

Find the limit. $$ \lim _{x \rightarrow-2} x^{3} $$

Short Answer

Expert verified
The limit as \(x\) approaches \(-2\) of the function \(x^{3}\) is \(-8\).

Step by step solution

01

Identify the Function

The function given in the exercise is \(f(x) = x^{3}\). This function is continuous for all real numbers, which means the limit as \(x\) approaches any number exists and is simply \(f\) of that number.
02

Substitute the Limit Point

Substitute \(x = -2\) into the given function. Calculate \(f(-2)\), which is the value of the function at the point \(-2\). This is done as follows: \(f(-2) = (-2)^{3} = -8\).
03

Evaluate the Limit

Since we have calculated the value of the function at \(-2\) and the function is continuous at this point, the limit as \(x\) approaches \(-2\) of the function \(x^{3}\) is simply \(f(-2)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An environmental study indicates that the average daily level \(P\) of a certain pollutant in the air, in parts per million, can be modeled by the equation \(P=0.25 \sqrt{0.5 n^{2}+5 n+25}\) where \(n\) is the number of residents of the community, in thousands. Find the rate at which the level of pollutant is increasing when the population of the community is 12,000 .

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ f(x)=\frac{1}{\left(x^{2}-3 x\right)^{2}} $$

Use the General Power Rule to find the derivative of the function. $$ y=\sqrt[3]{9 x^{2}+4} $$

You deposit in an account with an annual interest rate of \(r\) (in decimal form) compounded monthly. At the end of 5 years, the balance is \(A=1000\left(1+\frac{r}{12}\right)^{60}\) Find the rates of change of \(A\) with respect to \(r\) when (a) \(r=0.08\), (b) \(r=0.10\), and (c) \(r=0.12\).

Find an equation of the tangent line to the graph of \(f\) at the point \((2, f(2)) .\) Use a graphing utility to check your result by graphing the original function and the tangent line in the same viewing window. $$ f(x)=x \sqrt{x^{2}+5} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.