Question

Determine if the limit exists, and if it does, find its value.

(5/x-1) -(5/3)/(x-4)
lim
x→4

Answer 1

\[\lim_{x \to4}\dfrac{5}{x-1}=\dfrac{5}{3}\] but \[\lim_{x \to 4}\dfrac{\frac{5}{3}}{x-4}=\infty\] so the limit doesn't exist.