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Analysis: Limits, strictly increasing, differentiability

  1. Nov 16, 2011 #1

    Shackleford

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    I've worked all of these out. I'm mostly confident I did them correctly, but I'm prone to overlook subtleties or counterexamples sometimes.

    http://i111.photobucket.com/albums/n149/camarolt4z28/1ab-1.png [Broken]

    http://i111.photobucket.com/albums/n149/camarolt4z28/1gf2-1.png [Broken]
     
    Last edited by a moderator: May 5, 2017
    Shackleford, Nov 16, 2011
  2. jcsd
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  3. Nov 16, 2011 #2

    SammyS

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    1. b is false.

    Is f(x) positive ?

    I'll look at the other problem soon.
     
    SammyS, Nov 16, 2011
  4. Nov 16, 2011 #3

    Shackleford

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    Oh. You're saying the limit could be negative infinity, too, not just positive infinity. That's true.
     
    Shackleford, Nov 16, 2011
  5. Nov 16, 2011 #4

    SammyS

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    Or, f(x) could alternate from large positive to large negative values as x → ∞.
     
    SammyS, Nov 16, 2011
  6. Nov 16, 2011 #5

    SammyS

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    The second link looked OK to me.
     
    SammyS, Nov 16, 2011
  7. Nov 16, 2011 #6

    Shackleford

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    Good catch on (b). Thanks for the review!
     
    Shackleford, Nov 16, 2011
  8. Nov 16, 2011 #7

    deluks917

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    Its possible your professor wants you to write out your steps a bit more.
     
    deluks917, Nov 16, 2011
  9. Nov 16, 2011 #8

    Shackleford

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    For which ones?
     
    Shackleford, Nov 16, 2011
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