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Simple limits problem

  1. Sep 15, 2006 #1
    I'm given the limit f(x + [tex]\Delta[/tex]x) / [tex]\Delta[/tex]x
    Given f(x) is 2x + 3, do I just plug in 2x +3 into x? Or do I plug it into x and [tex]\Delta[/tex]x, or do I find the limits of f(x + [tex]\Delta[/tex]x) / [tex]\Delta[/tex]x) and -f(x)/[tex]\Delta[/tex]x?, etc..If someone could get me started on this it would be great, Thanks.
     
  2. jcsd
  3. Sep 15, 2006 #2

    arildno

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    First of all, write your problem CORRECTLY from your book. That you haven't done.
     
  4. Sep 15, 2006 #3
    This is my first time using latex so I guess I'll just type it out for clarity. Find the limit of the function (f(x + delta x) - f(x)) / delta x as delta x approaches 0 when f(x) = 2x + 3.
     
  5. Sep 15, 2006 #4

    arildno

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    Quite so.
    Given that, what is in this case f(x+delta x)?
     
  6. Sep 16, 2006 #5

    HallsofIvy

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    You are going to find it very, very difficult to do calculus if you don't understand what "f(x)" and "f(x+ y)" mean!

    If f(x)= 2x+ 3, then f(a)= 2a+ 3 (just replace x in the entire formula with whatever is in the parentheses on the left). In particular, f(x+ y)= 2(x+ y)+ 3= 2x+2y+ 3.

    (Your latex was fine in your first post. arildno's point was that you didn't specify "as [itex]\Delta[/itex]x goes to 0"!)
     
  7. Sep 16, 2006 #6

    arildno

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    Actually, he did not subtract f(x) in the numerator; that's what I reacted upon.
     
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