\lim_{x\to0} \frac{4^{3x}-1}{x}=

AP ICET 2015 Paper

Question : 135 of 200

Marks: +1, -0

\lim↙{x→0}\;\;{4^{3x}-1}/{x}=

Solution:

\lim↙{x→0}\;\;{4^{3x}-1}/{x}

=\lim↙{x→0}{(4^{3})^{x}-1}/{x}=\lim↙{x→0}{64^{x}-1}/{x}

=\log_{e}64=\log_{e}4^{3}=3\log_{e}4

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