Can you limit the floor?

Calculus Level 2

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

\(\displaystyle A. \lim_{x \to 5^+}f(x)=1\)

\(\displaystyle B. \lim_{x \to 5^-}f(x)=0\)

\(\displaystyle C. \lim_{x \to 5^+}f(x)=4\)

\(\displaystyle D. \lim_{x \to 5^-}f(x)=1\)

\(\displaystyle E. \lim_{x \to 5^+}f(x)=0\)

\(\displaystyle F. \lim_{x \to 5}f(x) \text{does not exist}\)

\(\displaystyle G. \lim_{x \to 5}f(x) \text{exists}\)

Details:

  • (\(\lfloor \cdot \rfloor\)) denotes floor function
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