Question

vertical asymptotes

Answer 1

Use graphs and tables to find the limit and identify any vertical asymptotes of \[\lim_{x \rightarrow 7}1/(x-7)^2\]

Answer 2

@zepdrix I need you again! these asymptotes are really throwing me off... you probably hate me by now :(

Answer 3

\[\Large \lim_{x\to7}\frac{1}{(x-7)^2}\]

Graphs and tables? Hmm.

Answer 4

Yeah!! isn't that a weird question??? LOL wth

Answer 5

This is something you'll want to get comfortable with.\[\Large \frac{1}{x}\]Look at the above expression.
As x gets closer to zero (let's say from the right), the term is getting closer and closer to infinity.

Here is how that works.
Let's plug in a value really close to zero and see what happens.\[\Large x=\frac{1}{999999} \qquad\qquad \frac{1}{x}\qquad=\qquad\frac{1}{\left(\dfrac{1}{99999}\right)}\]Remember what we do when we divide fractions? We flip the bottom one.\[\Large =\frac{99999}{1}\]Which is a really big number, heading towards infinity.

Answer 6

I know ^ that isn't exactly what you're looking for, but it's kind of important to understand if you want to get a grasp on asymptotes.

Answer 7

So for our problem here.. hmm

Answer 8

Let's just do the cheater way I guess.. let's make a table :3

Answer 9

We'll make a table, choosing like... 3 values on the right, getting closer and closer to x=7 each time.

Then we'll choose 3 values on the left, getting closer and closer to x=7 each time.

Answer 10

So what we're doing is, we're imitating the limiting process ourselves.
We're going to plug in values and see what happens as we get closer and closer.

Answer 11

ok cool so if we plug that in we get 100!

Answer 12

Ok good, let's get a little bit closer to 7 with our next value.

Answer 13

ok 10000 :D

Answer 14

Sounds good, let's get really really close now :3

Answer 15

100000000 :D

Answer 16

omg haha

Answer 17

Ok good :) so we've determined that when we approach 7 from the right side, we're approaching positive infinity, right?

Answer 18

LOL bajilion xD and Yeah we are approaching infinity and 6.9 gives us 100 too!?

Answer 19

positive 100? :OO that's weird!!