Question

PLEASE HELP WILL GIVE A MEDAL
Use graphs and tables to find the limit and identify any vertical asymptotes of

Answer 1

you want the numerical method, I guess?

Answer 2

numerical *approach....
k, shoot the question.

Answer 3

So you want to fill in the table.
\(\large\color{black}{ \huge{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr f(x) \\
\hline
\scr~~~8.0~ & \scr 0 \\
\hline
\scr~~~8.5~ & \scr 0 \\
\hline
\scr~~~8.9~ & \scr 0 \\
\hline
\scr~~~8.99~ & \scr 0 \\
\hline
\scr~~~8.999~ & \scr 0 \\
\hline \end{array} } }\)

Answer 4

i don't understand @SolomonZelman

Answer 5

that would be the table to fill in to find \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~9^-}f(x)}\) .

Answer 6

You are basically finding the output, for numbers that approach 9 from the left side.

Answer 7

it doesn't have to use those specific numbers, but you would want to choose a bunch of numbers that are close to 9, and getting closer and closer to 9.

Answer 8

but dont you just keep getting numbers close to -1 for f(x)

Answer 9

you want the numbers close to 9, because you are finding the \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~9^-}~\frac{1}{x-9}}\)

Answer 10

\(\large\color{slate}{\displaystyle\frac{1}{\color{blue}{8}-9}=\frac{1}{-1}=-1}\)

\(\large\color{slate}{\displaystyle\frac{1}{\color{blue}{8.5}-9}=\frac{1}{-0.5}=-2}\)

\(\large\color{slate}{\displaystyle\frac{1}{\color{blue}{8.9}-9}=\frac{1}{-0.1}=-10}\)

\(\large\color{slate}{\displaystyle\frac{1}{\color{blue}{8.99}-9}=\frac{1}{-0.01}=-100}\)

\(\large\color{slate}{\displaystyle\frac{1}{\color{blue}{8.999}-9}=\frac{1}{-0.001}=-1000}\)

Answer 11

See, as I am plugging numbers closer and closer to 9 (from the left side) we get an input that closer and closer approaches negative infinity.

Answer 12

wait so 9 or -9

Answer 13

you are finding \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~9^-}\frac{1}{x-9}}\)

Answer 14

I was plugging numbers for x (that approach 9 from the left) , that is all.

Answer 15

so the vertical asymptote is 9?

Answer 16

yes.

Answer 17

oh okay thank you!

Answer 18

do you fully understand why though?

Answer 19

yes through plugging the numbers in we see that

Answer 20

basically, the idea here is:

\(\large\color{slate}{\displaystyle\frac{1}{x-9}}\).

as x is approaching 9 from the right, the x will be a little greater than 9.
NOW, the closer x gets to 9 (from right side) thesmaller decimal you get on the denominator.

Answer 21

1 / infinitely small (positive) decimal

is same thing as infinity

Answer 22

So your graph, you can already make.