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At which points the function \mathrm{f(x)=\frac{x}{[x]}} ,where [.] is greatest integer function, is discontinuous 

 

Option: 1

only positive integers

 


Option: 2

all integer and (0, 1)

 


Option: 3

all rational numbers 


Option: 4

none of these


Answers (1)

best_answer

(i)  When \mathrm{0 \leq x<1} 

        \mathrm{f(x)} doesn’t exist as [x] = 0 here.

(ii)  Also \mathrm{\lim _{x \rightarrow I+} f(x) \text { and } \lim _{x \rightarrow I-} f(x)}   does not exist.

Hence \mathrm{f(x)}  is discontinuous at all integers and also in (0, 1)

 

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Nehul

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