anonymous
  • anonymous
How would I solve this?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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SolomonZelman
  • SolomonZelman
\(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~7^-}~\dfrac{1}{x-7}}\)
SolomonZelman
  • 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

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SolomonZelman
  • SolomonZelman
So, this way you should be able to identify the asymptote.
anonymous
  • anonymous
So, B?
SolomonZelman
  • 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: \(\large\color{slate}{\displaystyle\lim_{x \rightarrow ~7~^-}~\dfrac{1}{x-7}}\)
SolomonZelman
  • 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".
anonymous
  • anonymous
-1 -2 -10 -100 -1000
SolomonZelman
  • SolomonZelman
yes.... see where the limit is going as x approaches 7 closer and closer?
anonymous
  • anonymous
-infinity
SolomonZelman
  • SolomonZelman
yes, this limit is going towards -∞
SolomonZelman
  • SolomonZelman
Any questions?
anonymous
  • anonymous
Unless you're willing to help me with another problem, no.
SolomonZelman
  • SolomonZelman
Oh, ok. But in different post if you will. (i will see if I can make it there)
anonymous
  • anonymous
Thank you.
SolomonZelman
  • SolomonZelman
anytime!

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