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Grade: 12
        
If f(x) =(1+|sinx|) ^(a÷|sinx|)   , -π÷6
           =b                                     , x=0
           =e^(tan2x÷tan3x)         , 0
Find a and b so that the function is continuous at x=0
8 months ago

Answers : (1)

Aditya Gupta
1236 Points
							
RHL= e^(2/3) coz tan2x/tan3x can be written as tan2x/2x*3x/tan3x*2/3 and lim y tends to zero tany/y=1
So b=e^(2/3)
For LHL, put |sinx|= z
Then we have (1+z)^a/z= e^a
So a=2/3
8 months ago
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