The function is L(t)=8.4sin((2pi/365)(t-80))+12.6
How would I go about finding the L'(t)? Should I simply multiply within the parenthesis and then multiply that with 8.4sin or is there another way to go about it?
-m
it's just the chain rule:
$\displaystyle \frac d{dx}f(g(x)) = f'(g(x)) \cdot g'(x)$
thus, $\displaystyle L'(t) = 8.4 \cos \left( \frac {2 \pi}{365}(t - 80) \right) \cdot \left( \frac {2 \pi}{365}(t - 80) \right)'$
now find $\displaystyle \left( \frac {2 \pi}{365}(t - 80) \right)'$ and plug it in
no, the derivative of sine is cosine
not sure about the estimate part. i would have probably directly computed the integral (it's actually not that hard), but i suppose that's not want you want. i'm trying to remember if there is any rule or theorem that allows us to estimate integrals, but nothing in this context is coming to mind... what do your notes/text say?And if so, the next part of the question asked that I use a graph of L(t) to obtain a rough estimate of $\displaystyle \int{L(t)}dt$ from 0 to 80. How should I go about estimating this problem?