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Limit of Functions and Tyalor's theorem

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data
    The problem is attached with this message.
    Here is the direct link of the image: http://picasaweb.google.ca/lh/photo/8QB5XydAGZP4jIXfej9lsw?authkey=x-xog63oZxw

    2. Relevant equations
    for problem B I know I need to use Taylor's theorem. But I am not sure how to get started?

    3. The attempt at a solution

    For problem A I think I need to assume 1/x=y and the y-> infinity, is this right direction?

    BTW Tan represents the principle branch of tangent function.

    Attached Files:

    Last edited: Dec 3, 2008
  2. jcsd
  3. Dec 3, 2008 #2
    Your image isnt working for me perhaps to explain the problem in text
  4. Dec 3, 2008 #3
    updated the message, there is adirect link to the image now.
  5. Dec 4, 2008 #4


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    Homework Helper
    Gold Member

    For part A, you should know that [itex]\tan^{-1}(+\infty)=\frac{\pi}{2}[/itex], so your limit is of the form [itex]\frac{0}{0}[/itex] and you can use l'Hopital's rule.

    For B;if f'(x)=f(x), then f''(x)=__? And so f'''(x)=__?And so.....:wink:
  6. Dec 4, 2008 #5


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    This clearly is not "pre" calculus so I am moving it to "Calculus and Beyond".
  7. Dec 4, 2008 #6
    I got part a abd b of part B but now I am stuck at proving that it is bounded by [0,x] and after that I think I know. But if you can help me with that that would be great!
  8. Dec 4, 2008 #7
    What does it mean for f(x) to be bounded on [0,x]?
  9. Dec 5, 2008 #8
    It means there exists a value M such that |f(y)| ≤ M for all y in [0,x].
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