Question

Planet Quirk. PS3, Part II, 3a. The result I am getting is that dL/dh is always less than
or equal to delta L over delta h. The question states I should explain the opposite
(i.e. delta L/delta h <= dL/dh). I have calculated dL/dh = h/L, delta L = L(h0+delta h) - L (h0).
if I take h0 = 20000 and delta h = 1 I get delta L/delta h = 200.002/1=200.002 and dL/dh = 20001/200.002 = 100.003

Am I getting this wrong?

Answer 1

Same applies for h=20001 + delta h (where detlta h= 1, 1/10, 1/100). For h=25000+delta h I get dL/dh equal to delta L/delta h.

Answer 2

it seems I got it. I should have evaluated dL/dh at 25000 and 20001 (i.e. at h0 not h0+delta h).

Answer 3

Yes, they say "if the derivative is evaluated at the left-endpoint of the interval"
the x-interval is from x0 to x0+\(\Delta\)
and the "left end-point" is x0
That is, we assume we are on the number line (or x-axis)
and x0+\(\Delta\) is to the right of x0 for positive Δ

Answer 4

thanks phi. these planet quirk problems make me crazy. :-) just trying to understand now why the accuracy of L decreases as h0 approaches the point below the sattelite. i.e. it turns out the closer I am to that point the larger my delta L is which is very confusing. In real life the common sense says the closer i am to the object the more accurate my measurements of that object are likely to be.

Answer 5

A picture might help