Problem

Sketch the graph of an example of a function $ f …

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Problem 14 Easy Difficulty

Use the graph of the function $ f $ to state the value of each limit, if it exists. If it does not exist, explain why.
(a) $ \displaystyle \lim_{x \to 0^-}f(x) $
(b) $ \displaystyle \lim_{x \to 0^+}f(x) $
(c) $ \displaystyle \lim_{x \to 0}f(x) $

$ \displaystyle f(x) = \frac{x^2 + x}{\sqrt{x^3 + x^2}} $

Name: use the graph of the function f to state the value of each limit if it exists if it does not exist 2
Uploaded: 2017-09-08
Duration: 1 min 56 s
Channel: Numerade
Description: Use the graph of the function $ f $ to state the value of each limit, if it exists. If it does not exist, explain why. (a) $ \displaystyle \lim_{x \to 0^-}f(x) $ (b) $ \displaystyle \lim_{x \to 0^+}f(x) $ (c) $ \displaystyle \lim_{x \to 0}f(x) $ $ \displaystyle f(x) = \frac{x^2 + x}{\sqrt{x^3 + x^2}} $

Answer

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Topics

Limits

Derivatives

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

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Video Transcript

Mrs Problem number fourteen Stuart, eighth edition, section two point two He's the graph of the function F to state the value of each limit. If it exists, it is not explain why. So we take a look at their plot using neither crapping calculator Ah, this Excel spreadsheet or any other graphing the tool. And we take this function and plot it and we're gonna be planting around X equals zero because that is the location of interest. And to answer party the limit of this as experts zero from the left, we see that the behavior you Raph approaching through from the left is equal to negative one. And that is the left hand limit. Take a look at the graph again, per p. The limit of F as experts zero from the right. We follow the behavior of the function and we see that it approaches approximately one positive one as we traced the function from the right zero towards zero. Finally, the limit as expert is zero of the function AF has to do with both the left hand lemon and the right hand woman. They both exist, but they are not in agreement. Make it one on one are different parts of the graph and therefore we say that the limit had, as experts zero in totality does not exist.

Daniel J.

Topics

Limits

Derivatives

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Problem

Sketch the graph of an example of a function $ f …

Problem 14 Easy Difficulty

Answer

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Heather Z.

Kayleah T.

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Watch More Solved Questions in Chapter 2

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Heather Z.

Kayleah T.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos