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Question

limx0log cosxx=


Solution

We have, limx0log cosxx

At x=0,the value of the expression is the form 00

applying L'Hospital Rule

                                               limx0ddx(log cosx)ddxx

= limx01cos x.ddxcosx1

                                                   = limx01cos x(sin x)

                                                     limx0tan x

putting x=0

=-tan 0=0.

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