The value of a for which the function `f(x)=f(x)={((4^x-1)hat3)/(sin(x a)log{(1+x^2 3)}),x!=0 12(log4)^3,x=0` may be continuous at `x=0` is 1 (b) 2 (c) 3 (d) none of these

Explanation

`f(x)=f(x)=((4^x-1)^3)/(sin(x /a)log{(1+(x^2)/ 3)}]`


`lim_(x→0)​f(x)=f(0)=12(log4)^3`


`=lim_(x→0)​((4^x-1)^3)/(x^3) (x/a)/(sin(x /a)) (ax^2​)/log(1+x^2/3​)`



`=(log4)^3alim​_(x→0)(x^2)/(x^2/3+...)`

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