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L'Hospital Rule

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img692.imageshack.us/img692/6661/36979008.jpg [Broken]

    2. Relevant equations

    3. The attempt at a solution
    whats wrong with it? im 100% sure and i can explain each one!
    the first one equals 3 right?

    second one should be true cuz 0/0 can be any number.. (thats what my teacher from high school said at least)
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 17, 2009 #2
    Then you just answered your own question. :-)
  4. Nov 17, 2009 #3
    yeah but i guess i think that i know everything but something might be wrong..
    and it will take me a long time to write down an explanation for each one :/

    is the 3rd one right? i mean, f/g has to be g cannot = 0.. but its not in the lhospital rule...
  5. Nov 17, 2009 #4
    someone please help me
  6. Nov 17, 2009 #5


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    Science Advisor

    What exactly is your question? In your first post you said "im 100% sure and i can explain each one!"

    The only question I can find is in your second post, "is the 3rd one right? i mean, f/g has to be g cannot = 0.. but its not in the lhospital rule... " In order that we be able to use L'Hospital's rule directly, we must have [itex]\lim_{x\to a} g'(x)\ne 0[/itex] and that's impossible if g'(x)= 0 in some neighborhood of a. We might be able to extend L'Hopital's rule in the case that f'/g' goes to 0/0 itself by using L'Hopital's rule again, but in order for that to work eventually, there must be some nth derivative of g which has non-zero limit at x= a but again, that's impossible if there is some neighborhood of a in which g' is 0.
  7. Nov 17, 2009 #6
    my question is, which one from the picture above is wrong?
    Last edited: Nov 18, 2009
  8. Nov 18, 2009 #7
    please someone!! i checked it over like 20 times now..
    1. is 'false' for sure cuz it limit = 3
    2. its a fact so 'true'
    3. its a rule so 'true'
    4. its part of the rule so 'true'
    5. small number / big number = closer and closer to 0 ==> 0 so 'true'
    6. limit of infinity = infinity.. :| so 'true'
    7. like the 3rd one but in words, so 'true'

    whats wrong with it??
  9. Nov 18, 2009 #8
    point 4. g'(x) must be nonzero in some interval that contains c. This should be:
    in every interval that contains c, g'(x) can't be zero everywhere in that interval.
  10. Nov 18, 2009 #9


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    Gold Member

    I would reconsider number 6. Just think about what would happen if [itex]\lim_{x \to \infty}f(x) = -\infty[/itex].
  11. Nov 19, 2009 #10
    those are such small things that both me and 2 of my buddies didnt pick on.. oh man. :|

    thanks guys
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