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Let f(x)=⎪ ⎪⎪ ⎪(1+|sinx|)a|sinx|,x6<x<0           b,x=0        etan 2x / tan 3x,0<x<π6 then the value of a and b if f is continuous at  x=0, are respectively
  1. None of these


Solution

The correct option is D

f(x)=⎪ ⎪⎪ ⎪(1+|sinx|)a|sinx|,x6<x<0b,x=0etan 2x / tan 3x,0<x<π6 
For f(x) to be continuous at x = 0

limx0f(x)=f(0)=limx0+f(x)

limx0(1+|sinx|)a|sin x|=elimx0(|sin x|a|sin x|)=ea.

Now,limx0+etan 2xtan 3x=c limx0+.e(tan 2x2x×2x) / (tan 3x3x×3x)

=limx0+e23=e23
 

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