1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: It's a limit question
  1. Limit question (Replies: 2)

  2. Limit question (Replies: 3)

  3. Limit question (Replies: 9)

  4. Limit question (Replies: 1)

  5. A limit question (Replies: 7)

Loading...