Answer
$-\infty$
Work Step by Step
As x approaches the value 2,
the numerator approaches a positive finite number 100,
the denominator becomes a very small negative number.
We note two things:
(1) the quotient is negative (a positive is divided by a negative number),
(2) the quotient's absolute value becomes very large (grows infinitely), because we divide an (almost) constant number with smaller and smaller to extremely small numbers.
This brings us to conclude that
$\displaystyle \lim_{x\rightarrow 2}\frac{f(x)}{g(x)}=-\infty$.
