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Let \mathrm{f(x)=[x] \sin \left(\frac{\pi}{[x+1]}\right)}where [ ] denotes the greatest integer function. Then the points of discontinuity of \mathrm{f(x)} in its domain are :

Option: 1

all integers 


Option: 2

all integers \mathrm{ -\{1\} }


Option: 3

all integers \mathrm{ -\{-1\}}


Option: 4

all integers \mathrm{ -\{0\}}


Answers (1)

best_answer

\mathrm{ f(x)=[x] \sin \left(\frac{\pi}{[x+1]}\right)}
\mathrm{ So, \quad[x+1] \neq 0 \Rightarrow[x] \neq-1 \, \, \, \, \, So, \quad x \neq[-1,0)}
\mathrm{Domain R-[-1,0)}.\\ \mathrm{Possible\, \, points\, \, of \, \, discontinuity \, \, are\, \, x= Integers -\{-1\}}.
\mathrm{f(0)=0, \lim _{x \rightarrow 0^{+}} f(x)=0 \text { so continuous at } x=0 \text {. }}.
 

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