anonymous
  • anonymous
Help with calculus!
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\frac{ \lim }{ x \rightarrow-7^{+} }f(x)=-\infty \]Graph this.
jim_thompson5910
  • jim_thompson5910
how far did you get?
jim_thompson5910
  • jim_thompson5910
I'm going to start a blank xy graph. Add to the graph what you have so far |dw:1441237470407:dw|

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jim_thompson5910
  • jim_thompson5910
click the pencil on my drawing to be able to draw on it
anonymous
  • anonymous
I couldn't figure out where to start.
anonymous
  • anonymous
How can you draw infinity?
jim_thompson5910
  • jim_thompson5910
ok let's start by plotting a point at -7 on the x axis |dw:1441237530533:dw|
jim_thompson5910
  • jim_thompson5910
then draw a vertical dashed line through -7 |dw:1441237577069:dw|
jim_thompson5910
  • jim_thompson5910
the limit says "as x gets closer and closer and closer to -7 from the right side, the value of y heads off to negative infinity" so there are a number of ways to do this. You could have something like this |dw:1441237684271:dw|
jim_thompson5910
  • jim_thompson5910
or something like this |dw:1441237697243:dw|
jim_thompson5910
  • jim_thompson5910
or maybe something like this |dw:1441237713578:dw| the majority of this graph doesn't matter as long as you approach -infinity as you get closer to -7 from the right side
anonymous
  • anonymous
Oh..that makes much more sense. Can you check my answers for some others? I think I might have them wrong.
jim_thompson5910
  • jim_thompson5910
sure
anonymous
  • anonymous
Thanks so much!\[\frac{ \lim }{ x \rightarrow5^{+} }f(x)=-8\]
anonymous
  • anonymous
|dw:1441237595205:dw|
anonymous
  • anonymous
That's what I put but I don't think it's right...
jim_thompson5910
  • jim_thompson5910
I'm going to delete the horizontal line |dw:1441237965993:dw|
jim_thompson5910
  • jim_thompson5910
the idea here is that as we get closer to x = 5 from the right side, the y value gets closer to -8 so here is one way to do it |dw:1441238039952:dw|
jim_thompson5910
  • jim_thompson5910
here is an alternative way |dw:1441238056519:dw|
anonymous
  • anonymous
So there is no line coming from the right?
jim_thompson5910
  • jim_thompson5910
just like before, the majority of it doesn't matter as long as you end up at y = -8 when you approach from the right side of x = 5
jim_thompson5910
  • jim_thompson5910
`So there is no line coming from the right?` what do you mean?
anonymous
  • anonymous
*left
anonymous
  • anonymous
I meant left sorry.
jim_thompson5910
  • jim_thompson5910
oh, that could be possible, yes you could have |dw:1441238163678:dw| or |dw:1441238177135:dw| and I'm just realizing that your example is perfectly valid. You can approach x = 5 from the right and end up getting closer and closer to y = -8
anonymous
  • anonymous
So why do they need a plus next to the 5 under the limit?
jim_thompson5910
  • jim_thompson5910
that notation means "right hand limit" since we're approaching from the right side of that x value
anonymous
  • anonymous
So how does that apply to the graph?
jim_thompson5910
  • jim_thompson5910
for right hand limits, you don't need to worry about the left side so that's why we could stop at x = 5 and not continue on
jim_thompson5910
  • jim_thompson5910
it allows us to graph more variety we could have graphs that stop at x = 5 or we could have graphs that continue on
anonymous
  • anonymous
Okay I'm going to go with your answer just in case.
anonymous
  • anonymous
\[\frac{ \lim }{ x \rightarrow \infty }f(x)=4\]
Zarkon
  • Zarkon
a little \(\LaTeX\) help for you \[\lim_{ x \to\infty }f(x)=4\] \lim_{ x \to\infty }f(x)=4
anonymous
  • anonymous
|dw:1441238256310:dw|
anonymous
  • anonymous
What is Latex?
jim_thompson5910
  • jim_thompson5910
it's a tool to help write math notation
anonymous
  • anonymous
Oh...
jim_thompson5910
  • jim_thompson5910
that graph you drew is correct here is another possible answer for the limit \[\Large \lim_{x\to\infty}f(x) = 4\] |dw:1441238706491:dw|
jim_thompson5910
  • jim_thompson5910
and another possible answer |dw:1441238735088:dw| the idea is to get closer to that horizontal line as x gets larger
jim_thompson5910
  • jim_thompson5910
of course, we could cross that horizontal line like this |dw:1441238767240:dw| but notice how we still approach that horizontal line as x gets bigger
anonymous
  • anonymous
Okay so if the number under the limit is + or - that number, would I just extend the line like what I did on the second problem?
jim_thompson5910
  • jim_thompson5910
I'm not sure what you mean
jim_thompson5910
  • jim_thompson5910
you mean like that \(\Large 5^{+}\) notation?
anonymous
  • anonymous
Ya the notation on the top. If it is + and - (left and right) would you extend the line across the graph like what I did in the 2nd problem I gave?
jim_thompson5910
  • jim_thompson5910
It's possible to extend it through, but also just as valid to stop at that x value. Both interpretations are valid for that one-sided limit If you were talking about a 2-sided limit, then you would have to extend it through because you would be approaching that x value from both sides (left and right)
jim_thompson5910
  • jim_thompson5910
|dw:1441239084919:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1441239111134:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1441239138986:dw|
anonymous
  • anonymous
Okay I understood that. Last one:\[\left(\begin{matrix}\lim \\ x \rightarrow-\infty\end{matrix}\right)f(x)=-2\]
anonymous
  • anonymous
|dw:1441238954330:dw|
anonymous
  • anonymous
Sorry the drawing board was malfunctioning
anonymous
  • anonymous
It's suppose to be a straight line
jim_thompson5910
  • jim_thompson5910
one last thing though, it's possible to evaluate a one-sided limit on a connected curve. Just approach from one side |dw:1441239320678:dw|
anonymous
  • anonymous
Ohh ya! I forgot about that.
jim_thompson5910
  • jim_thompson5910
as for your other problem, as long as you're approaching y = -2 as x heads off to negative infinity, then you have the proper graph another valid answer is this |dw:1441239584767:dw|
jim_thompson5910
  • jim_thompson5910
something like this is also possible |dw:1441239609022:dw|
anonymous
  • anonymous
Okay thanks! That's all I needed. :)
jim_thompson5910
  • jim_thompson5910
you're welcome

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