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L' HOPITAL rule in solving limit problems.

B.Sudhakar
29/12/2016 0 1

L'HOPITAL rule : Applicable to all limit problems wherein both numerator and denominator becomes either '0' or '∞'   like 0/0 or ∞/∞ after substituting limiting value.

As per this method, we need to differentiate both numerator and denominator and then substitute limiting value to et an answer.

Ex: LIM x>0 sin x/x, on substituting 0 to variable 'x' to both numerator and denominator we get indeterminate form 0/0 ( sin 0 = 0).

Now differentiating both numerator & denominator wrt 'X' we get  LIM x>0 cos x/1 (derivative of sin x=cos x and derivative of x = 1) now by substituting 0 to variable 'x' we get cos 0/1= 1/1 = 1( as cos 0=1) and that is the answer using L'HOPITAL rule. 

 

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Karthik | 30/12/2016

Thank you sumeru I found this very useful. I was all the time wondering when L' hospital rule should be applied. The example you have posted cleared my doubt.

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