Can you limit the floor?

Calculus Level 2

Let f(x)=x29x+20xx,\displaystyle f(x) = \frac{x^2-9x+20}{x-\lfloor x \rfloor}, then which of the following are correct?

A. limx5+f(x)=1B. limx5f(x)=0C. limx5+f(x)=4D. limx5f(x)=1E. limx5+f(x)=0F. limx5f(x)  does not existG. limx5f(x)  exists\begin{array}{c}&\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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