Derivative of floor function?

Calculus Level 2

Find $\displaystyle \lim_{x \to2}\lfloor{x}\rfloor$ .

Notation : $\lfloor \cdot \rfloor$ denotes the floor function .

Does not exist -2 2 0

1 solution

Paul Ryan Longhas
Jul 25, 2016

As $x \rightarrow 2^- \implies 1 < x < 2$ that is $\lfloor x \rfloor = 1$ . Also, as $x \rightarrow 2^+ \implies 2 < x < 3$ that is $\lfloor x \rfloor = 2$ .

So, the limit of $RHS \neq LHS$ that is the limit does not exist.

Derivative of floor function?

1 solution

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