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stop swindling asked in Science & MathematicsMathematics · 9 years ago

Evaluate difference quotient for given function?

f(x) = 1/x, f(x)-f(a)/x-a

I tried but cannot get the answer -1/xa. I can get the denominator but niot the numerator. Can you help me?

2 Answers

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  • Ed I
    Lv 7
    9 years ago
    Favorite Answer

    [f(x) - f(a)]/(x - a) = [1/x - 1/a]/(x - a) = [a - x)/(ax)]/(x - a) = -1/ax

    As x --> a, the difference quotient approaches -1/a^2.

  • ben e
    Lv 7
    9 years ago

    [1/x - 1/a]/[x - a]

    [a/(ax) - x/(ax)]/[x - a]

    1/(ax)*[a - x]/[x - a]

    1/(ax)*(-1)

    -1/(ax)

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