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?

\[\begin{array} &\text{A. } \lim_{x \to 5^+}f(x)=1 &&&\text{B. } \lim_{x \to 5^-}f(x)=0\\ \text{C. } \lim_{x \to 5^+}f(x)=4 &&&\text{D. } \lim_{x \to 5^-}f(x)=1\\ \text{E. } \lim_{x \to 5^+}f(x)=0 &&&\text{F. } \lim_{x \to 5}f(x)\ \text{ does not exist}\\ \text{G. } \lim_{x \to 5}f(x)\ \text{ exists} & \end{array}\]

Notation: \(\lfloor \cdot \rfloor\) denotes the floor function.

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