If a function defined by f (x )= (3^x-1)^2 sin ⁡ xlog ⁡ (1+x ) ,x 0, is continuous at x=0, then f (0 )=

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Correct answer: D. (b) Given f (x )= (3^x-1)^2 sin ⁡ xlog ⁡ (1+x ) ,x 0 Now, lim_x 0f (x )= lim_x 0 0.05em (3^x-1)^2 sin ⁡ xlog ⁡ (1+x ) = limx 0 0.05em ( 3^x-1x )^2 sin ⁡xx log ⁡ (1+x )x= ( log ⁡3 )^21 1= ( log ⁡3 )^2 Since f (x ) is continuous at x=0 So lim_x 0f (x )=f (0 ) ⇒f (0 )= ( log ⁡3 )^2

$If a function defined by f (x) = \frac{( 3 ^{x} - 1 ) ^{2}}{sin xlog ( 1 + x )}, x \neq = 0, is continuous at x = 0, then f (0) =$

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