The value of \lim_{x \to 0} {a^{x}-b^{x}}/{x} is

BPSC 53-55th Exam Prelims 17 Apr 2011 Solved Paper

Question : 80 of 150

Marks: +1, -0

The value of

\lim ↙{x → 0} \;{a^{x}-b^{x}}/{x}

Solution:

\lim ↙{x → 0} \;{a-b}/{x}

\lim ↙{x → 0}[\;{a^{x}-1}/{x}-\;{b^{x}-1}/{x}]

=\log _{e}(a)-\log _{e}(b)

=\log _{e} \;{a}/{b}

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