Find the limit by interpreting the expression as an appropriate derivative.
lim [(10^h)-1]/h
h-->0
I've been staring at this problem forever and don;t know where to begin, please help!
Find the limit by interpreting the expression as an appropriate derivative.
lim [(10^h)-1]/h
h-->0
I've been staring at this problem forever and don;t know where to begin, please help!
Are you allowed to use L'Hospital's Rule?
$\displaystyle \displaystyle \begin{align*} \lim_{h \to 0}\frac{10^h - 1}{h} &= \lim_{h \to 0}\frac{\frac{d}{dh}\left(10^h - 1\right)}{\frac{d}{dh}\left(h\right)} \\ &= \lim_{h \to 0}\frac{10^h\ln{(10)}}{1} \\ &= \ln{(10)}\lim_{h \to 0}10^h \\ &= \ln{(10)}\cdot 10^0 \\ &= \ln{(10)} \cdot 1 \\ &= \ln{(10)} \end{align*} $