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Question

limx0x loge x will be equal to ___


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Solution

We can observe that

As x0 ,logex

So if we write the above expression as logex1x then,

as x0, 1x;logex1xreduces to () form.

So we can use L’Hospital Rule. We are doing all this because direct substitution of x as zero is not giving us the limit.

So L’Hospital Rule states that limxaf(x)g(x)=limxaf(x)g(x)

So for logex1x taking derivative of numerator and denominator we get 1x1x2

So limx0logex1x=limx01x1x2=limx0(x)=0 which is the correct answer.


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