Question
Consider the function f(x) = \(\frac{x^{2}-4}{x-2}\)
(a) Find .
(b) Is continuous at ? Explain why or why not.
▶️Answer/Explanation
(a) We can simplify the function by factoring the numerator:
\(f(x) = \frac{(x-2) -(x+2)}{x-2}=x+2\)
Now, we can find the limit:
(b) No, is not continuous at . The function is undefined at because it would result in division by zero.