Question

Single Choice If [] denotes the greatest integer function, lim sin(cos.x] (cos.x]+2 is: () denotes greatest integer function) Α Ο D Does not exist

JEE/Engineering Exams

Maths

Solution

101

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( lim _{x rightarrow pi / 2} frac{5 sin [cos x]}{[cos x]+2} quad operatorname{RHL} x rightarrow pi / 2 quad cos x rightarrow 0^{-} ) ( L H L lim _{x rightarrow infty} x rightarrow pi / 2 quad cos x rightarrow 0^{+} quad ) i.e. ( [cos x]=-1 ) ( i cdot e cdot[cos x] Rightarrow 0 quad therefore R H L=frac{5 operatorname{sen} t 1}{-1+2} Rightarrow L H C ) ( therefore L H L=frac{5 sin 0}{0+2}=0 ) (D) doesnot exist