Question
Evaluate the following Limits:
$\lim _{x \rightarrow 0}\left[\frac{a^{3 x}-a^{2 x}-a^x+1}{x^2}\right]$
$\lim _{x \rightarrow 0}\left[\frac{a^{3 x}-a^{2 x}-a^x+1}{x^2}\right]$
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(ii) $\left|\begin{array}{ccc}1 & 2 x & 4 x \\ 1 & 4 & 16 \\ 1 & 1 & 1\end{array}\right|=0$
$\lim _{x \rightarrow 0}\left[\frac{\log 100+\log (0.01+x)}{x}\right]$