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  • Let <img alt="\mathrm{f(x)=\left\{\begin{array}{ll}\frac{[\sin x]}{[x]}, & {[x] \neq 0} \\ 1, & {[x]=0}\end{array}\right. ([.] }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmat

Let \mathrm{f(x)=\left\{\begin{array}{ll}\frac{[\sin x]}{[x]}, & {[x] \neq 0} \\ 1, & {[x]=0}\end{array}\right. ([.] }denotes the greatest integer function), then set of integral values of x for which f is not differentiable, is

Option: 1

set of all integers
 


Option: 2

set of all non-zero integers
 


Option: 3

set of all positive integers
 


Option: 4

set of all negative integers


Answers (1)

best_answer

\mathrm{\text { Clearly for }-1<x<0}

\mathrm{\frac{[\sin x]}{[x]}=\frac{-1}{-1}=1 \text { and for } 0 \leq x<1, f(x)=1}

\mathrm{\text { So } f(x) \text { is differentiable at } x=0 \text {, but at other integers }[x] \text { will change. }}

Posted by

Suraj Bhandari

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