lim imet-e *–2x 2A is equal to x+0 ...
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lim imet-e *–2x 2A is equal to x+0 X-sin x (a) 1 (c)2 (b)-1 (d) 0

JEE/Engineering Exams
Maths
Solution
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( lim _{x rightarrow 0} frac{e^{x}-e^{-x}-2 x}{x-sin x} ) ( int frac{0}{0} ) form a Apply I thopital's rule ( lim _{x rightarrow 0}left[frac{e^{x}+e^{-x}-2}{1-cos x}right] ) idgain ( frac{0}{0} ) form, applying ( L^{prime} ) teopital's ( lim _{x rightarrow 0}left[frac{e^{x}-e^{-x}}{sin x}right] ) again ( frac{0}{0} ) form, apply ( L^{prime} ) Hopital's ( lim _{x rightarrow 0}left[frac{e^{x}+e^{-x}}{cos x}right] ) ( frac{e^{0}+e^{0}}{cos 0}=frac{1+1}{1} ) 2 j Obtion ce) is correct.
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