Determine if a function is continuous

  • Context: MHB 
  • Thread starter Thread starter kendalgenevieve
  • Start date Start date
  • Tags Tags
    Continuous Function
Click For Summary

Discussion Overview

The discussion centers around the continuity of a piecewise function at the point x = -2. Participants are analyzing the limit of the function as x approaches -2 and its value at that point to determine continuity.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents the piecewise function and asks whether it is continuous at x = -2.
  • Another participant states that to ensure continuity, the limit as x approaches -2 must equal the function's value at that point, which they propose should be 4.
  • A different participant calculates the limit and claims to have found it to be -4, suggesting that it does not equal 4.
  • A subsequent reply agrees with the calculation of -4 and concludes that this indicates the function is not continuous at x = -2.

Areas of Agreement / Disagreement

There is disagreement regarding the limit of the function as x approaches -2, with one participant asserting it is -4, while another suggests it should be 4. The discussion remains unresolved regarding the continuity of the function.

Contextual Notes

Participants have not explicitly defined the conditions under which the limit is evaluated, and there may be assumptions about the behavior of the function near x = -2 that are not fully explored.

kendalgenevieve
Messages
6
Reaction score
0
$$f(x)=\begin{cases}\dfrac{x^2-4}{x+2}, & x\ne-2 \\[3pt] 4, & x=-2 \\ \end{cases}$$

Determine if its continuous at x=-2
 
Last edited by a moderator:
Physics news on Phys.org
To ensure continuity, we require:

$$\lim_{x\to-2}\frac{x^2-4}{x+2}=4$$

Is this true?
 
MarkFL said:
To ensure continuity, we require:

$$\lim_{x\to-2}\frac{x^2-4}{x+2}=4$$

Is this true?

I just got -4 so no it does not equal 4
 
Hi kendalgenevieve! Welcome to MHB! ;)

kendalgenevieve said:
I just got -4 so no it does not equal 4

Good!
That means it's not continuous.
 

Similar threads

MHB Finding k for x is undefined at $x=2$
  • · Replies 3 ·
Replies
3
Views
1K
MHB 217 AP Calculus Exam continous function with k
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Idea about single-point differentiability and continuity
  • · Replies 1 ·
Replies
1
Views
2K
MHB Understanding Continuous Functions: Examining f'(7) Undefined
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Uniform convergence of family of functions with continuous index
  • · Replies 3 ·
Replies
3
Views
2K
MHB Find f'(0) from a piecewise function
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Continuity of Mean Value Theorem
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Understanding a proof of inexistence of max nor min
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Extreme value nonexistence proof
  • · Replies 11 ·
Replies
11
Views
2K