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Find the limit if it exists: lim h approaching 0 f(7 + h) - f(7) over h. For f(x) = -x + 1?

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Find the limit if it exists: lim h approaching 0 f(7 + h) - f(7) over h. For f(x) = -x + 1?

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  1. lim[(1 - (x + h)) - (1 - x)] / h =

    h→0

    lim[1 - x - h - 1 + x] / h =

    h→0

    lim[- h] / h = - 1 for all x

    h→0

    lim[(1 - (7 + h)) - (1 - 7)] / h =

    h→0

    lim[(1 - 7 - h - 1 + 7] / h =

    h→0

    lim[- h] / h = - 1

    h→0

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