Question

Problem Set 1, Part II, 2.a) Is delta_L/delta_h supposed to be positive for all the delta_h? I'm also having a little trouble understanding what delta_L/delta_h means.

Answer 1

It looks like they want to take the absolute value of
\[ \Delta L = L - L_0 \]

L is a function of h, specifically
\[ L(h) = \sqrt{ h^2 - (2.0e4)^2} \]
if we change h, we will get a change in L.
the ratio \( \frac{ΔL}{Δh} \) tells us the change in L relative to the change in h
if this ration is large, it means a small change in h causes a large change in L (L is *sensitive* to changes in h). Or if it is small (much less than 1), then L changes only a little with changes in h. L would be *insensitive* or *robust* with respect to changes in h.