calculus

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find lim x->0 3- sqrt x+9/-x

  • calculus -

    In general, when there is a sum or difference of square-root terms, multiplying both numerator and denominator by the conjugate is a good strategy.

    Lim (3- sqrt( x+9))/(-x )
    x->0
    = Lim (3-sqrt(x+9))(3+sqrt(x+9))/[(-x)(3+sqrt(x+9)]
    x->0
    = Lim (9-(x+9))/[(-x)(3+sqrt(x+9)]
    x->0
    = Lim (-x)/[(-x)(3+sqrt(x+9)]
    x->0
    = Lim 1/(3+sqrt(x+9)
    x->0
    =1/6

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