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Question

If the function f(x)=(1+|sinx|)a|sinx|,π6<x<0b,x=0etan2xtan3x,0<x<π6, is continuous at x = 0, then

A
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C
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Solution

The correct option is C
LHL=limx0f(x)=limh0f(0h)=limh0(1+(sin(h)))a|sin(h)|=limh0(1+sinh)a|sin(h)|=elimh0(1+sinh1)a|sin(h)|=eaRHL=limx0+f(x)=limh0f(h)=limh0etan2htan3h=elimh023.tan2h2h.3htan3h=e23V.F.=f(0)=bb=e23=eaa=23,b=e23 or a=logeb

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