Question

find the limit and identify any vertical asymptotes the function.

Answer 1

looks impossible to me.

Answer 2

Jajaja, its hard. You just need to expand the (x-10). Do you know how to?

Answer 3

yes!

Answer 4

(x-10)(x-10)?

Answer 5

Expand it and plug o=x

Answer 6

(10-10)(10-10) = 0?

Answer 7

No, \[x ^{2}-20+100\]

Answer 8

Observe the following after I substitute x = 10:\[\bf \lim_{x \rightarrow 10}1=\frac{ 1 }{ (x-10)^2 }=\frac{1}{(10-10)^2}=\frac{1}{0}=\infty\]This also implies that x = 10 is the vertical asymptote.

@kjuchiha

Answer 9

Sorry i wrote the limit incorrectly. the equal sign and 1 in the beginning are not supposed to be there lol.

Answer 10

So holy... the limit is infinity?

Answer 11

sorry, \[\frac{ 1 }{ x ^{2}-20x+100 }\]

Answer 12

yup

Answer 13

No, Plug in x onto the formula I gave

Answer 14

100-2000 + 100 = 1/2000

Answer 15

O no it doesnt work!

Answer 16

Yeah, I think we should graph it!

Answer 17

The limit is infinity whereas the vertical asymptote is x=10.

Answer 18

Yeah, it goes to infinity

Answer 19

Whenever you get\[\bf \frac{ x }{ 0 }, \ x >0\] after the substitution, the function approaches positive infinity at that x-value.

Whenever we have:\[\bf \frac{ x }{ 0 }, \ x < 0\] after the substitution, the function approaches negative infinity at that x-value.

And if we get 0/0, then that's an indeterminate form and we must tackle the limit differently.

@kjuchiha

Answer 20

anything over 0 = infinity?

Answer 21

I see!!

Answer 22

Thank you all so so much. I finally get to go to sleep.

Answer 23

Night all

Answer 24

sweet dreams. i hope you see me bowling and getting a hat trick in your dreams.

Answer 25

LOL you're crazy

Answer 26

g'night lmao!

Answer 27

Here is a graph