\(\displaystyle \mbox{Given that }\, f(x)\, \mbox{ is defined by }\, f(x)\, =\, \begin{cases} \dfrac{(4^x\, -\, 1)^3}{\sin\left(\dfrac{x}{p}\right)\, \log\left(1\, +\, \dfrac{x^2}{3}\right)} & \mbox{for }\, x\, \neq\, 0 \\ \left. \right. & \mbox{ } \\ 12\, \left(\ln(4)\right)^3 & \mbox{for }x\, =\, 0 \end{cases}\)
\(\displaystyle \mbox{find the value of }\, p\, \mbox{ for which }\, f(x)\, \mbox{ is continuous at }\, x\, =\, 0.\)
\(\displaystyle \mbox{find the value of }\, p\, \mbox{ for which }\, f(x)\, \mbox{ is continuous at }\, x\, =\, 0.\)
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