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Math Help - One Sided Limit

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    One Sided Limit

    limit as x→3 from the left of Square root (9-x^2)
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    Quote Originally Posted by rawkstar View Post
    limit as x→3 from the left of Square root (9-x^2)
    Notice that y = \sqrt{9 - x^2}

    y^2 = 9 - x^2

    x^2 + y^2 = 3^2.


    This is a circle of radius 3 centred at (0,0).

    Therefore its domain is x \in [-3, 3].

    Since x is defined approaching 3 from the left, we can simply substitute x = 3 into the equation.


    So \lim_{x \to 3}\sqrt{9 - x^2} = \sqrt{9 - 3^2} = \sqrt{0} = 0.
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