If , where denotes the greatest integer less than or equal to ,…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x)=\begin{cases}\frac{\sin[x]}{[x]},&[x]\ne0\\0,&[x]=0\end{cases}

, where

[\cdot]

denotes the greatest integer less than or equal to

x

, then: (1)

\lim_{x\to0}f(x)=\sin1

(2)

\lim_{x\to0^+}f(x)=0

(3) The limit does not exist at

x=0

. (4) The limit exists at

x=0