Identify the correct statements.

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

Problem

Identify the correct statements. (1)

\lim_{n\to\infty}\left(\sum_{r=1}^{n}\frac{1}{2^r}\right)=1

(2) If

f(x)=(x-1)\{x\}

, where

\lfloor x\rfloor

and

\{x\}

denote the greatest integer function and fractional part of

x

, respectively, then the limit of

f(x)

does not exist at

x=1

. (3)

\lim_{x\to0^+}\left\lfloor\frac{\tan x}{x}\right\rfloor=1

(4)

\left\lfloor\lim_{x\to0^+}\frac{\tan x}{x}\right\rfloor=1