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Thread: 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 $\displaystyle y = \sqrt{9 - x^2}$

    $\displaystyle y^2 = 9 - x^2$

    $\displaystyle x^2 + y^2 = 3^2$.


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

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

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


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