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It's a limit question

  1. Jan 14, 2004 #1
    Here's a question from calc I (I'm currently in calc III). My cousin needs help with this problem and I'm truely clueless as of how to solve it. It's a limit question. The questions reads, As X approaches 0 what is the limit of f(x)=(1+.01x)^(10/x). I'm guessing something needs to be done with the power (10/x) but I'm not sure quite sure what.
     
  2. jcsd
  3. Jan 14, 2004 #2
    Apply the formula
    [tex]\lim_{x\rightarrow 0}(1+x)^{\frac{1}{x}}=e[/tex]
     
  4. Jan 14, 2004 #3
    [tex]
    \lim_{x\rightarrow 0} f(x) = \left(1 + 0.1x\right)^{\frac{10}{x}} = \left[\begin{array}{cc}
    t = \frac{1}{10x} \\ x =
    x \rightarrow 0 \Leftrightarrow t \rightarrow \infty
    \end{array}\right] = [/tex][tex]\lim_{t \rightarrow \infty}f(t) = \left(1 + \frac{0.1}{t}\right)^{t} = \ldots
    [/tex]

    Something with [tex]e[/tex]. If it would have been [tex]0.1x[/tex] instead of [tex]0.01x[/tex]...

    Nille
     
  5. Jan 15, 2004 #4
    it would be [tex]e^{\frac{1}{10}}[/tex]
     
  6. Jan 19, 2004 #5
    How about using the Binomial Exapnsion to re-write the expression and then looking at whether you can simplify it when x--> 0?
     
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