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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: solve this limit
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sourab_MCA (30)

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[x ][0 ] (sinx/x)sinx/(x-sinx)

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sandeepramesh (1247)

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L = lim x-> 0 [ 1 + (sinx - x /x) ]^(sinx/x-sinx) = e^-1 = 1/e
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studyid (1664)

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e to the power -1 i.e 1/e

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dream (571)

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can u please give me the method also
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ramkumar_november (1270)

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l   =  \lim_{x\to 0} \bigg(\frac{sinx}{x}\bigg)^{\frac{sinx}{x-sinx}}
 
l  =  \lim_{x\to 0} \bigg(1+\frac{sinx-x}{x}\bigg)^{\frac{sinx}{x-sinx}}
 
l  = \lim_{x\to 0} \bigg(1+\frac{sinx-x}{x}\bigg)^{\frac{x}{sinx-x}.\frac{-sinx}{x}}
 
l  =  e^{-1}
 
method already given by sandeepramesh.....
i just latexified it......
 
hope you are clear.........
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dream (571)

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ya
thanks
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