Help with calculus!

- anonymous

Help with calculus!

- Stacey Warren - Expert brainly.com

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- jamiebookeater

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- anonymous

\[\frac{ \lim }{ x \rightarrow-7^{+} }f(x)=-\infty \]Graph this.

- jim_thompson5910

how far did you get?

- 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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## More answers

- jim_thompson5910

click the pencil on my drawing to be able to draw on it

- anonymous

I couldn't figure out where to start.

- anonymous

How can you draw infinity?

- jim_thompson5910

ok let's start by plotting a point at -7 on the x axis
|dw:1441237530533:dw|

- jim_thompson5910

then draw a vertical dashed line through -7
|dw:1441237577069:dw|

- 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

or something like this
|dw:1441237697243:dw|

- 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

Oh..that makes much more sense. Can you check my answers for some others? I think I might have them wrong.

- jim_thompson5910

sure

- anonymous

Thanks so much!\[\frac{ \lim }{ x \rightarrow5^{+} }f(x)=-8\]

- anonymous

|dw:1441237595205:dw|

- anonymous

That's what I put but I don't think it's right...

- jim_thompson5910

I'm going to delete the horizontal line
|dw:1441237965993:dw|

- 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

here is an alternative way
|dw:1441238056519:dw|

- anonymous

So there is no line coming from the right?

- 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

`So there is no line coming from the right?` what do you mean?

- anonymous

*left

- anonymous

I meant left sorry.

- 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

So why do they need a plus next to the 5 under the limit?

- jim_thompson5910

that notation means "right hand limit" since we're approaching from the right side of that x value

- anonymous

So how does that apply to the graph?

- 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

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

Okay I'm going to go with your answer just in case.

- anonymous

\[\frac{ \lim }{ x \rightarrow \infty }f(x)=4\]

- Zarkon

a little \(\LaTeX\) help for you
\[\lim_{ x \to\infty }f(x)=4\]
\lim_{ x \to\infty }f(x)=4

- anonymous

|dw:1441238256310:dw|

- anonymous

What is Latex?

- jim_thompson5910

it's a tool to help write math notation

- anonymous

Oh...

- 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

and another possible answer
|dw:1441238735088:dw|
the idea is to get closer to that horizontal line as x gets larger

- 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

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

I'm not sure what you mean

- jim_thompson5910

you mean like that \(\Large 5^{+}\) notation?

- 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

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

|dw:1441239084919:dw|

- jim_thompson5910

|dw:1441239111134:dw|

- jim_thompson5910

|dw:1441239138986:dw|

- anonymous

Okay I understood that. Last one:\[\left(\begin{matrix}\lim \\ x \rightarrow-\infty\end{matrix}\right)f(x)=-2\]

- anonymous

|dw:1441238954330:dw|

- anonymous

Sorry the drawing board was malfunctioning

- anonymous

It's suppose to be a straight line

- 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

Ohh ya! I forgot about that.

- 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

something like this is also possible
|dw:1441239609022:dw|

- anonymous

Okay thanks! That's all I needed. :)

- jim_thompson5910

you're welcome

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