Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.
A$0$
B$1$
C$\ln a$
D$a$
Answer & Solution
Correct answer: C. $\ln a$
A fundamental limit is $\lim_{x\to 0}\dfrac{a^x-1}{x}=\ln a$. It is closely related to the derivative of $a^x$ at $x=0$.
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