If - is a root of the equation sin x-1-x then lim x -min sin x-x-x-1- isWhere - - denotes greatest integer functionx- fractional part of xA- 0B- Does not existC- -1D- 1

The correct option is B Does not exist LHL x→α ^ lim [ min(sin x,x [x])/(x 1) ] When 1 lt;x lt;α {x}=x 1 lt;sin x min{sin x, x 1}=x 1 Required limi ...

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Standard XII

Mathematics

Properties of Determinants

If α is a roo...

Question

If $α$ is a root of the equation $s i n x + 1 = x$ then $l i m x \to \infty [\frac{m i n (s i n x, {x})}{x - 1}]$ is
Where $[.] \to$ denotes greatest integer function
${x} \to$ fractional part of x.

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Does not exist

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-1

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Solution

The correct option is B Does not exist

LHL
$l i m x \to α^{-} [\frac{m i n (s i n x, x - [x])}{(x - 1)}] W h e n 1 < x < α {x} = x - 1 < s i n x m i n {s i n x, x - 1} = x - 1 R e q u i r e d l i m i t = l i m x \to \infty^{-} [\frac{x - 1}{x - 1}] = 1 x \to α + s i n x < x - 1 \frac{s i n x}{x - 1} < 1 R H L : l i m x \to α + [\frac{s i n x}{x - 1}] = 0 H e n c e L H L \neq R H L L i m i t d o e s n o t e x i s t [\frac{s i n x}{x - 1}] = 0$

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If α is a root of the equation sinx+1=x then limx→∞[min(sinx,{x})x−1] is Where [.]→ denotes greatest integer function {x}→ fractional part of x.

The correct option is B Does not exist LHL limx→α−[min(sinx,x−[x])(x−1)]When 1<x<α{x}=x−1<sinxmin{sinx,x−1}=x−1Required limit=limx→∞−[x−1x−1]=1x→α+sinx<x−1sinxx−1<1RHL:limx→α+[sinxx−1]=0Hence LHL≠RHLLimit does not exist[sinxx−1]=0

If $α$ is a root of the equation $s i n x + 1 = x$ then $l i m x \to \infty [\frac{m i n (s i n x, {x})}{x - 1}]$ is
Where $[.] \to$ denotes greatest integer function
${x} \to$ fractional part of x.