Question

Lim of - (x-9)/root(x) -3 as x approaches 9

Answer 1

You know conjugation?

Answer 2

yes, i get 0? but i am not sure.

Answer 3

will i have to do Lopitals?

Answer 4

yes as it is 0/0 form you can apply lhospitals rule.

Answer 5

but wont i get 0/9 since i did the conjugate?

Answer 6

nevermind, i got it why

Answer 7

do i take the derivative of the original equation? or the conjugated one?

Answer 8

Ooopsie. I see a better solution.
Is it
\[\lim_{x \rightarrow 9}-\frac{ (x-9) }{ \sqrt{x}-3 } \]

Answer 9

yes that is the original

Answer 10

Okay okay.
Do you know that\[x-9 = (\sqrt{x} - 3)(\sqrt{x}+3)\]

Answer 11

And with that we can cancel one term which is \[\sqrt{x}-3\]

Answer 12

Hence our limit will then become
\[\lim_{x \rightarrow 9} - (\sqrt{x}+3)\]

Answer 13

Do you get my point?

Answer 14

Yes, so we are allowed to do that?

Answer 15

Of course :))

Answer 16

iget -6?

Answer 17

That's right.

Answer 18

but it doesn't seem like it has a limit of -6?