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calculus

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What is the limit as x approaches infinity of radical (9x*2+x)-3x?

  • calculus - ,

    I assume you mean
    radical (9x²+x)-3x
    Multiply top and bottom by the conjugate

    [√(9x²+x)-3x]
    =[√(9x²+x)-3x]*[√(9x²+x)+3x] / √[(9x²+x)+3x]
    =(9x²+x-9x²)/[√(9x²+x)+3x]
    =x/[√(9x²+x)+3x]

    Now evaluate the limit as x->∞
    Lim x/[√(9x²+x)+3x]
    = x / 6x
    = 1/6

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