-*°12 -COS X then the value If L = ...
Question
Fullscreen

-*°12 -COS X then the value If L = lim x+0 Ĉ then the value of 1/(3L) is: X- 0 x sin x

JEE/Engineering Exams
Maths
Solution
125
Rating
4.0 (1 ratings)
Fullscreen
( frac{e^{-x^{2} / 2}-cos x}{x^{3} sin x} ) applying L'Hopital ( frac{-x e^{-x^{2} / 2}+sin x}{3 x^{2} sin x+x^{3} cos x} ) Applying L'Hopital again, ( lim _{x rightarrow 0} frac{x^{2} e^{-x^{2}+2}-e^{-x^{2} / 2}+cos x(+1-1)}{3 x^{2} cos x+6 x sin x+3 x^{2} cos x-x^{3} sin x} ) Dividing numerator and denomenater by ( x ) ( lim _{x rightarrow 0} frac{e^{-x^{2} / 2}-left(e^{-x^{2}+2}-1right)-(1-cos x)}{(-1)left(-frac{x^{2}}{2}right) times 2}-frac{x^{2}}{3 cos x+6left(frac{sin x}{x}right)+3 cos x-x sin x} ) ( v_{0} L=frac{1+frac{1}{2}-frac{1}{2}}{3+6+3-0}=frac{1}{12} ) ( log (1 / 3 L)=4 quad Rightarrow operatorname{An} 1 )
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free