Question

What is the limit of y=x(9-x^2)^(1/2) as x approaches 3^- (AKA from the left)

Answer 1

\[\lim_{x\to 3^{-}}x\sqrt{9-x^2}\]?

Answer 2

Yes, that is it.

Answer 3

since \(x<3\) you are in the domain of this function
as \(x\to 3^-\) we have \(x^2\to 9\) and so \(9-x^2\to 0\) and likewise \(\sqrt{9-x^2}\to 0\)

Answer 4

so your answer should be 0

Answer 5

What was the process you used to yield that answer? Could you explain it? I'm not following is it is neither the dividing out method nor the rationalizing method.

Answer 6

easier than that
this is a product
\(3\times 0=0\)

Answer 7

So simply plugging in 3 would do the trick? No catch?