Question

Question part points submissions used consider the following. g(x)={((x**2-a**2)/(x-a) text(if ) x != a,4 text(if ) x =

Answer 1

For $x\neq a$, we have

$\dfrac{x^2-a^2}{x-a}=\dfrac{(x-a)(x+a)}{x-a}=x+a$

So for $g(x)$ to be continuous at $x=a$, we require that the limit as $x\to a$ is equal to 4.

$\displaystyle\lim_{x\to a}g(x)=\lim_{x\to a}(x+a)=2a=4\implies a=2$