If \( \lim _{x \rightarrow a} f(x)=\lim _{x \rightarrow a}[f(x)](a \) is a finite quantity), whe...

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If \( \lim _{x \rightarrow a} f(x)=\lim _{x \rightarrow a}[f(x)](a \) is a finite quantity), where [.] denotes greatest integer function and \( f(x) \) is a non constant continuous function, then :
(a) \( \lim _{x \rightarrow a} f(x) \) is an integer
(b) \( \lim _{x \rightarrow a} f(x) \) need not be an integer
(c) \( f(x) \) has a local minimum at \( x=a \)
(d) \( f(x) \) has a local maximum at \( x=a \)
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