Question 1
A function has a removable discontinuity at $x=2$. What does that mean most directly?
Question 2
For $f(x)=\frac{x^2-4}{x-2}$ when $x\neq 2$, what value should be assigned to $f(2)$ to make $f$ continuous at $x=2$?
Question 3
Why is the discontinuity of $g(x)=\frac{\sin x}{x}$ at $x=0$ removable?
Question 4
Which condition must be true for a discontinuity at $x=a$ to be removable?
Question 5
Suppose $h(x)=\frac{x^2-9}{x-3}$ for $x\neq 3$. Which statement is true about $h$ at $x=3$?
