If , where denotes the greatest integer function, and is a non-constant continuous…

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

Problem

\lim_{x\to a}f(x)=\lim_{x\to a}[f(x)]

, where

[\cdot]

denotes the greatest integer function, and

f(x)

is a non-constant continuous function, then (1)

\lim_{x\to a}f(x)

is irrational (2)

\lim_{x\to a}f(x)

is non-integer (3)

f(x)

has a local maximum at

x=a

(4)

f(x)

has a local minimum at

x=a