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Math Help - limits

  1. #1
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    limits

    Does anyone know how to solve this????

    If f(x)=2x−7 find


    lim
    h→ 0

    f(x+h)−f(x)
    h
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  2. #2
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    Quote Originally Posted by samtheman17 View Post
    Does anyone know how to solve this????

    If f(x)=2x−7 find


    lim
    h→ 0

    f(x+h)−f(x)
    h
    f(x) = 2x - 7

    f(x + h) = 2(x + h) - 7

     = 2x + 2h - 7.


    f(x + h) - f(x) = 2x + 2h - 7 - (2x - 7)

     = 2h.


    So \frac{f(x + h) - f(x)}{h} = \frac{2h}{h} = 2.


    Thus

    \lim_{h \to 0}\frac{f(x + h)- f(x)}{h} = \lim_{h \to 0}2 = 2.
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