Can you limit the floor?

Calculus Level 2

Let $\displaystyle f(x) = \frac{x^2-9x+20}{x-\lfloor x \rfloor},$ then which of the following are correct?

Notation: $\lfloor \cdot \rfloor$ denotes the floor function.

Select one or more

\lim_{x\to5^+} f(x) = 1

\lim_{x\to5^-} f(x) = 0

\lim_{x\to5^+} f(x) = 4

\lim_{x\to5^-} f(x) = 1

\lim_{x\to5^+} f(x) = 0

\lim_{x\to5^+} f(x) \text{ does not exist}

\lim_{x\to5} f(x) \text{ exists}