Question

How would I solve this?

Answer 1

\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~7^-}~\dfrac{1}{x-7}}\)

Answer 2

well, you know (I would assume) that when you are dealing with a function
f(x)=1/(x-a)
then, your asymptote is x=a

Answer 3

So, this way you should be able to identify the asymptote.

Answer 4

So, B?

Answer 5

Now, you are asked to use a numerical approach (and make a table of values) for this limit.
I will show you what to do, and you will complete the chart:

keep in mind, your function is \(f(x)=\dfrac{1}{x-7}\)
and in your limit, the x is appraching 7 from the left side, so we start from values that are smaller than 7 just a bit, and then approach 7 closer and closer "from the left".

\(\large\color{black}{ \huge{ \begin{array}{| l | c | r |}
\hline \scr~~~x~~ & \scr~~~ f(x) ~~~\\
\hline
\scr~~~6~ & \scr ~ \\
\hline
\scr~~~6.5~ & \scr ~ \\
\hline
\scr~~~6.9~ & \scr ~ \\
\hline
\scr~~~6.99~ & \scr ~ \\
\hline
\scr~~~6.999~ & \scr ~ \\
\hline \end{array} } }\)

and using this table you should be able to find the limit: \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~7~^-}~\dfrac{1}{x-7}}\)

Answer 6

u can use wolframalpha.com to calculate these values for the table.
and these values don't need to be exactly those, just some values that closer and closer approach 7 "from the left".

Answer 7

-1
-2
-10
-100
-1000

Answer 8

yes....
see where the limit is going as x approaches 7 closer and closer?

Answer 9

-infinity

Answer 10

yes, this limit is going towards -∞

Answer 11

Any questions?

Answer 12

Unless you're willing to help me with another problem, no.

Answer 13

Oh, ok. But in different post if you will. (i will see if I can make it there)

Answer 14

Thank you.

Answer 15

anytime!