$l i m x \to 1 \frac{x s i n {x - [x]}}{x - 1}$ , where [.] denotes the greatest integer function, is

- 1

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Not existent

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None of these

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Solution

The correct option is B Not existent
$l i m x \to 1 \frac{x s i n {x - [x]}}{x - 1} R H L = l i m h \to 0 \frac{(1 + h) s i n {1 + h - [1 + h]}}{1 + h - 1} = l i m h \to 0 \frac{(1 + h) s i n (1 + h - 1)}{h} = 1 L H L = l i m h \to 0 \frac{(1 - h) s i n {1 - h - [1 - h]}}{1 - h - 1} = l i m h \to 0 \frac{(1 - h) s i n (1 - h)}{- h} = \infty L H L \neq R H L$

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