# 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
×