Answer
Jump discontinuity
Work Step by Step
a) At $x=0$, the numerator is equal to 0 and the denominator is equal to 0.
This could be a jump discontinuity where the function has different left and right limits.
b) $f(-0.1)=-0.708287$
$f(-0.01)=-0.707119$
$f(-0.0001)=-0.707107$
$\lim\limits_{x \to 0^-}=-0.707107$
$f(0.1)=0.708287$
$f(0.01)=0.707119$
$f(0.0001)=0.707107$
$\lim\limits_{x \to 0^-}=0.707107$
These values confirm our answer to part (a)
