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calculus

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Evaluate

lim as x-> 0

square root (x+1) - square root (2x+1)
/ square root (3x+4) - square root (2x+4)

  • calculus -

    multiply by [√(3x+4) + √(2x+4)]/[√(3x+4) + √(2x+4)][(√x+1) + √(2x+1)]/[(√x+1) + √(2x+1)]

    Expand only the factors which are the difference of squares pattern, leaving the other one alone.
    Your limit should reduce to
    -1([√(3x+4) + √(2x+4)]/[(√x+1) + √(2x+1)]
    which as x --->
    = -1(√4+√4)/(√1+√1)
    = -2

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