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Need some help with limits

  1. Sep 24, 2006 #1
    I am doing these practice problems to study for a test and I just can't figure them out, it's kind of frustrating.

    The first concerns the delta-epsilon proof.

    f(x) = 2-(1/x)
    x is approaching 1, and the limit is 1.
    Epsilon is given at 0.1

    so, what I have...
    0<|x-1|<d (delta)
    |f(x)-1|<.1
    so
    |2-(1/x)-1|<.1
    |1-(1/x)|<.1

    Maybe I am just an idiot, but how do I go from there?
    The answer is delta=1/11, I just can't see how to get it...

    I mean, I have done other problems like it,
    like for lim x->3 (2x-5) L=1 e=.01
    |2x-5-1|<.01
    2|x-3|<.01
    |x-3|<.005 so delta=.005

    And this other problem:
    find the limit, using algebra, for x->0 of sin7x/sin9x

    I multiplied both sides by csc9x, to get (sin7x*csc9x)/1
    because sinx*cscx=1, sin9x*csc9x=1

    But I can figure out where to go from there.
    Am I doing it wrong?

    Thank you for any help!
     
    Last edited: Sep 24, 2006
  2. jcsd
  3. Sep 24, 2006 #2
    Sorry to bother you guys, but can anyone explain to me how to find the standard equation of the tangent line to f(x) parallel to a given line? (so slope is known)

    I desperately need to know how to do this particular thing...

    Thanks!
     
    Last edited: Sep 24, 2006
  4. Sep 25, 2006 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Okay, so [itex]|\frac{x-1}{x}|< .1[/itex]
    You need to make |x-1|< 0.1|x|.
    If x is close to 1, how small can x be? How small must |x-1| be?

    Multiplied both sides of what by csc 9x? Looks to me like you just replaced 1/sin 9x by csc 9x.

    Anyway, do you know the limit of sin x/ x as x goes to 0?

    What would you do to get sin ax/x into that form?
     
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