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Let f(x)=x2−9x+20x−⌊x⌋,\displaystyle f(x) = \frac{x^2-9x+20}{x-\lfloor x \rfloor},f(x)=x−⌊x⌋x2−9x+20, then which of the following are correct?
A. limx→5+f(x)=1B. limx→5−f(x)=0C. limx→5+f(x)=4D. limx→5−f(x)=1E. limx→5+f(x)=0F. limx→5f(x) does not existG. limx→5f(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}C. limx→5+f(x)=4E. limx→5+f(x)=0G. limx→5f(x) existsA. limx→5+f(x)=1D. limx→5−f(x)=1F. limx→5f(x) does not existB. limx→5−f(x)=0
Notation: ⌊⋅⌋\lfloor \cdot \rfloor⌊⋅⌋ denotes the floor function.
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