Can you limit the floor?

Calculus Level 2

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

Notation: ⌊ ⋅ ⌋ \lfloor \cdot \rfloor denotes the floor function .

Select one or more

lim ⁡ x → 5 + f ( x ) = 1 \lim_{x\to5^+} f(x) = 1 lim ⁡ x → 5 − f ( x ) = 0 \lim_{x\to5^-} f(x) = 0 lim ⁡ x → 5 + f ( x ) = 4 \lim_{x\to5^+} f(x) = 4 lim ⁡ x → 5 − f ( x ) = 1 \lim_{x\to5^-} f(x) = 1 lim ⁡ x → 5 + f ( x ) = 0 \lim_{x\to5^+} f(x) = 0 lim ⁡ x → 5 + f ( x ) does not exist \lim_{x\to5^+} f(x) \text{ does not exist} lim ⁡ x → 5 f ( x ) exists \lim_{x\to5} f(x) \text{ exists}

Sparsh Sarode by Sparsh Sarode , 22, India

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