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Finding the limit of lim_(h-->0) (f(1+h,2) - f(1,2))/h

  1. Sep 9, 2004 #1
    I have a function [tex]z=2x^3+xy^2-6y[/tex]
    I need to find the limit of the following:
    [tex]\lim_{\substack{h\rightarrow 0}} \frac{f(1+h,2)-f(1,2)}{h}[/tex]
    I don't know if the function is required to calculate this limit, so I just wrote it as well. I just need some hint on where to begin, and how to approach this type of limit...
     
  2. jcsd
  3. Sep 9, 2004 #2

    Tide

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    Replace x and y with the specified values, expand your polynomials, subtract, look for cancellation and divide the result by h - then take your limit! :-)
     
  4. Sep 9, 2004 #3
    Won't I need to find the partial derivatives?
     
  5. Sep 9, 2004 #4

    Tide

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    That's exactly what you're doing.
     
  6. Sep 9, 2004 #5
    Hmm...I should replace x and y with the specified values, those are 1 and 2 ?
    If I do that in the function then I get the value -6. Where does that leave me?
     
  7. Sep 9, 2004 #6

    Tide

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    No, (x, y) = (1, 2) for f(1, h) but (x, y) = (1+h, 2) for f(1+h, 2).
     
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