Littlebird
  • Littlebird
Use the graph to estimate the limits and value of the function.
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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Littlebird
  • Littlebird
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Littlebird
  • Littlebird
I don't understand b. \[\lim_{s \rightarrow -2+} p(s) \]
theEric
  • theEric
I'm not sure I feel comfortable answering this, but I do know that the sign that is after \(2\) that looks like an exponent indicates the direction from which you approach the value that is \(p(s)\), which is \(p(-2)\) here. Since the limit is as \(s\rightarrow -2^+\), you are looking at approximating the limit from the positive side (where \(s\) is slighltly more positive than \(-2\). This is important with some asymptotes, maybe just hyperbolas, I know.|dw:1377651337227:dw|

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theEric
  • theEric
|dw:1377651448308:dw|
theEric
  • theEric
|dw:1377651483503:dw|
theEric
  • theEric
The first would be \(\infty\), while the second would be \(-\infty\), you agree? That's where direction of how you approach the limit is very important. Since those values are different, you know that that point couldn't be a nice, smooth flow where the point or limit would be found to be the same.
Littlebird
  • Littlebird
Is the limit 0? I got confused because the line on the right never has x=-2. Or are both lines part of one function, making the limit 3?
theEric
  • theEric
It looks like the function is continuous at \(s=-2\). Like, you can draw it without taking your pencil off of the paper. So the limit will by \(p(-2)\), as you see it on the graph, and it will be the same from both sides! Do you understand why?
Littlebird
  • Littlebird
If the limt is 3, then yes, I understand.
theEric
  • theEric
Then I believe we both understand the same! :) Congratulations!!!
Littlebird
  • Littlebird
Thanks :)
theEric
  • theEric
You are very welcome!

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