# Math Help - limits help

1. ## limits help

Find the limit by interpreting the expression as an appropriate derivative.
lim [(10^h)-1]/h
h-->0

2. ## Re: limits help please!

Originally Posted by calculuskangaroo
Find the limit by interpreting the expression as an appropriate derivative.
lim [(10^h)-1]/h
h-->0

Are you allowed to use L'Hospital's Rule?

\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*}

3. ## Re: limits help please!

thank you so much! can you just explain how you got from d/dh(10^h-1) to 10^h(ln10)
thank you!

4. ## Re: limits help please!

Originally Posted by calculuskangaroo
thank you so much! can you just explain how you got from d/dh(10^h-1) to 10^h(ln10)
thank you!
$\displaystyle \frac{d}{dx}\left(a^x\right) = a^x\ln{(a)}$, and the derivative of a constant is 0.

5. ## Re: limits help please!

ohhh okay! i got it now thank you so much