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

`lim_(x->0) (4^x - 1)^3/(sin(x-a)log(1+3x)) = 12(log4)^3`

now,`(e^(xln4) - 1)^3/(sin (x a)/(xa) xx log(1 + 3x^2))`

`= 1 + (xln4)/1 + (x ln4)^2/(2!) + (xln4)^3/(3!)+ .....`

`= ((1+ (xln4)/1 - 1)^3)/(ax log(1+3x^2)`

`= (x^3(ln4)^3)/(ax log(1+3x^2)`

`= (x^2(ln4))/(aln(1+3x^2) `

`= (ln4)^3/a xx x^2/(ln(1+3x^2))`

`= (2x/1)/(1/(1+3x^2)) xx 6x`

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