# Math Help - One Sided Limit

1. ## One Sided Limit

limit as x→3 from the left of Square root (9-x^2)

2. Originally Posted by rawkstar
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 $\lim_{x \to 3}\sqrt{9 - x^2} = \sqrt{9 - 3^2} = \sqrt{0} = 0$.