85 84 86 87 89 90 Single Choice +4/...
Question

# 85 84 86 87 89 90 Single Choice +4/-1 * 1 1 X-07 sin-x is equal to :

JEE/Engineering Exams
Maths
Solution
85
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( lim _{x rightarrow 0} frac{1}{x}-frac{1}{sin ^{2} x} ) Applying L-Hosfited Rulu (asitis ( left.frac{0}{0} text { form }right) ) ( lim _{x rightarrow 0} frac{sin ^{2} x-x^{2}}{x^{2} sin ^{2} x} ) ( lim _{x rightarrow 0} frac{2 sin x cos x-2 x}{2 x sin ^{2} x+sin 2 x} x= ) L-Hospilal Agoun Alpplying L-Hofosta Rulc ( lim _{x rightarrow 0} frac{2(0) 2 x-2}{2left[sin ^{2} x+x sin 2 xright]+2 x sin 2 x+2 cos 2 x cdot x^{2}} ) ( lim _{x rightarrow 0} frac{operatorname{lcos} 2 x-1}{sin ^{2} x+2 x sin 2 x+sin 2 x cdot x^{2}} ) Applying ( L-1400 ) kital Rule ( lim _{x rightarrow 0} frac{-2 sin 2 x^{2}}{sin 2 x+2[sin 2 x+2 cos 2 x cdot x]+left(-x^{2} cdot 2 sin 2 x+2 x cos 2 xright]} ) Pogajuro - fing Again applying L-Hospital Rulle ( left.lim _{x rightarrow 0} frac{-2 log 2 x}{left[2 cos 2 x+4 cos 2 x+4 cos 2 x-8 sin 2 x cdot x sin (x sin x) x-4 cos 2 x cdot x^{2}right.}+2 cos 2 x-4 sin 2 x cdot xright] ) Now linting ( x=0 ) ( frac{lim }{x rightarrow 0} frac{-4 x mid}{2 x|+4 x|+4 x mid-0-0-0+2-0}=frac{-4}{12}=frac{-1}{3} )