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Basic limit question

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data
    http://u1.imgupload.co.uk/1257984000/d192_image.gif


    2. Relevant equations
    above


    3. The attempt at a solution

    1st part should be okay for me and my ans is e^(2c)

    for the 2nd part, i have tried to use f'(x)=lim h-->infinity f(x+h)-f(x) / h and that just prove f'(x)=e but i found it maybe useless for finding c. so any hints can give me??

    or may i treat right side of the inquality as lim x--> infinity f(x) - lim x--> infinity f(x-1) ?

    thx:blushing:
     
  2. jcsd
  3. Nov 12, 2009 #2
    Look at the right hand side of your second part. Notice that it's

    limit as x gets large of: ( f(x) - f(x-1) ) / ( x - (x-1))

    If the actual derivatives of f are approaching a slope of e as x gets large, then what do you suppose is happening to slopes of secants measured way out there where x is very large?
     
  4. Nov 12, 2009 #3
    soory i cant get what you mean. may be it is too theoretic for me..
     
  5. Nov 13, 2009 #4
    Well, what is the form for the slope of a secant line to the graph of a function? How does that relate to the slope of the tangent line at some point?
     
  6. Nov 14, 2009 #5
    delete

    thx
     
    Last edited: Nov 14, 2009
  7. Nov 14, 2009 #6
    Well done!
     
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