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Limits and estimating slope

  1. Feb 16, 2006 #1
    Hey there, I need a little push in the right direction.
    Here is the question:
    The slope of the tangent line to the graph of the exponential function
    y=2^x at the point (0,1) is lim x approaches 0 (2^x-1)/x.
    Estimate the slope to three decimal places.
    Where I am getting confused is which formula do I plug (x) into to find a secant slope?
    I hope I asked the right question.
    Thanks
     
  2. jcsd
  3. Feb 16, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, since you are only asked to "estimate the slope to three decimal places" you just need to plug a small enough x into that secant formula which is exactly what you wrote: (2x-1)/x. That should take about 5 seconds using a calculator!

    (Finding the limit itself in order to find the actual formula is much harder!)
     
  4. Feb 17, 2006 #3
    Thank you for your help
     
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