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Rate of movement of glacier

  1. Oct 23, 2006 #1
    The movement of a certain glacier can be modelled by [tex]d(t)=0.01t^2+0.5t[/tex] where d is the distance in metres that a stake on the glaciers has moved, relative to a fixed position, t days after measurements began. Find the rate at which the glacier is moving after 20 days.

    What is the question asking for?

    I got an answer by using: lim_h-0 f(a+h)-f(a)/h

    and I got a final answer of 8.5 but the answer is 0.9m/day in the book !!!
  2. jcsd
  3. Oct 23, 2006 #2
    We could help you if you showed your work.
  4. Oct 23, 2006 #3
    [tex]d(t)=(0.01)t^2+0.5t, P(a,f(a))=(20,14)\\\lim_{h\rightarrow 0} \frac{(0.01(400-800h+h^2)+0.5(20+h)-14)}{h}\\
    \lim_{h\rightarrow 0} \frac{(0.01h^2+8.5h)}{h}=8.5

    Last edited: Oct 23, 2006
  5. Oct 23, 2006 #4
    I think it'll be simpler if you avoid the actual numbers till the last step.
    \lim_{\Delta t\rightarrow 0} \frac{\left(0.01\left(t + \Delta t\right)^2 + 0.5\left(t+\Delta t\right) \right) - \left(0.01t^2 + 0.5t\right)}{\Delta t}[/tex]

    Put t = 20 after you evaluate the limit.
  6. Oct 23, 2006 #5


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    Staff Emeritus
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    You're not going to like this!

    [itex](20+ h)^2= 400+ 2(20)h+ h^2= 400+ 40h+ h^2[/itex], not 800h!
    (You also have a "-" that should be there but that's obviously a typo since it didn't affect your final answer.)
  7. Oct 23, 2006 #6
    LMAO hallsofivy!!!

    Right now I'm laughing my ass off LMAO

    God damnit!!

    thanks....lol I GOT IT

    btw how do you put spaces in between tex stuff,,,....it says its \\ but it doesn't work...look at my tex
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