calculus

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Find the limit if it exists.

The limit of (sqrt(x+1)-2)/(x-3) as x tends to 3.

The limit of (sqrt(x+5)-sqrt(5))/x as x tends to 0

  • calculus -

    rationalize the numerator: I will do the first.

    Numerator: (sqrt(x+1)-2)(sqrt(x+1)+2_
    x+2-4=x-2 as x>3, it approaches 1
    Denominator: ((x-3)(sqrt(x+1)+2)
    xsqrt(x+1)+2x-3sqrt(x+1)-6
    as x>3
    3sqrt4+6-3sqrt(4)-6
    6+6-6-6 still zero.
    so you have as the limit 1/0, it does not exist.

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