MHB Determine if a function is continuous

[kendalgenevieve]

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

Determine if its continuous at x=-2

 

[MarkFL]

To ensure continuity, we require:

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

Is this true?

 

[kendalgenevieve]

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

 

[I like Serena]

Hi kendalgenevieve! Welcome to MHB! ;)

I just got -4 so no it does not equal 4

Good!
That means it's not continuous.