Question

find the limit if it exists lim of (2-x)/(x^2-4) as x approaches2

Answer 1

factor the denominator

Answer 2

\[\infty\]

Answer 3

\[\lim_{x\to 2}\frac{2-x}{x^2-4}=\lim_{x\to 2}\frac{2-x}{(x-2)(x+2)}\]

\[=\lim_{x\to 2}\frac{-(x-2)}{(x-2)(x+2)}=\lim_{x\to 2}\frac{-1}{(x+2)}=\frac{-1}{2+2}=\frac{-1}{4}\]