## anonymous one year ago How would I solve this?

1. anonymous

2. SolomonZelman

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

3. SolomonZelman

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

4. SolomonZelman

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

5. anonymous

So, B?

6. SolomonZelman

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

7. SolomonZelman

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".

8. anonymous

-1 -2 -10 -100 -1000

9. SolomonZelman

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

10. anonymous

-infinity

11. SolomonZelman

yes, this limit is going towards -∞

12. SolomonZelman

Any questions?

13. anonymous

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

14. SolomonZelman

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

15. anonymous

Thank you.

16. SolomonZelman

anytime!