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  • If     <img alt="\mathrm{f(x)=\left\{\begin{array}{r} \frac{\sin [x]}{[x]}, \text { for }[x]=0 \\ 0, \text { for }[x]=0 \end{array}\right.}" src="https://entrancecorner.oncodecogs.co

If     \mathrm{f(x)=\left\{\begin{array}{r} \frac{\sin [x]}{[x]}, \text { for }[x]=0 \\ 0, \text { for }[x]=0 \end{array}\right.}   where [] denotes greatest integer function.

     \mathrm{\lim _{x \rightarrow 0} f(x)} is equal to :

Option: 1

1


Option: 2

0


Option: 3

-1


Option: 4

None of these


Answers (1)

best_answer

Given function  \mathrm{{f(x)=\left\{\begin{array}{c} \frac{\sin [x]}{[x]}, \text { for }[x] \neq 0 0, \text { for }[x]=0 \end{array}\right.}}

we will evaluate right hand limit

\mathrm{ \lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0^{+}}[x]=0 \\ }

\mathrm{ \lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0} \frac{\sin [x]}{[x]}=\frac{\sin (-1)}{(-1)}=\sin 1 }

Limit does not exist.

Posted by

Anam Khan

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