The value of a for which the function `f(x)={(((4^x-1)^3)/(sin(x/a)log(1+x^2/3)) ,, x!=0),(12(log4)^3 ,, x=0):}` may be continuous at `x=0` is :

Options

A. (a) 1
B. (b) 2
C. (c) 3
D. (d)
none of these

Explanation

To determine the value of \( a \) for which the function

\[
f(x) =
\begin{cases}
\frac{(4^x - 1)^3}{\sin(x/a) \log(1 + x^2/3)} & \text{if } x \neq 0 \\
12(\log 4)^3 & \text{if } x = 0
\end{cases}
...