## anonymous one year ago Help with calculus!

1. anonymous

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

2. jim_thompson5910

how far did you get?

3. jim_thompson5910

I'm going to start a blank xy graph. Add to the graph what you have so far |dw:1441237470407:dw|

4. jim_thompson5910

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

5. anonymous

I couldn't figure out where to start.

6. anonymous

How can you draw infinity?

7. jim_thompson5910

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

8. jim_thompson5910

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

9. 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|

10. jim_thompson5910

or something like this |dw:1441237697243:dw|

11. 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

12. anonymous

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

13. jim_thompson5910

sure

14. anonymous

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

15. anonymous

|dw:1441237595205:dw|

16. anonymous

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

17. jim_thompson5910

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

18. 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|

19. jim_thompson5910

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

20. anonymous

So there is no line coming from the right?

21. 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

22. jim_thompson5910

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

23. anonymous

*left

24. anonymous

I meant left sorry.

25. 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

26. anonymous

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

27. jim_thompson5910

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

28. anonymous

So how does that apply to the graph?

29. 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

30. 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

31. anonymous

32. anonymous

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

33. Zarkon

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

34. anonymous

|dw:1441238256310:dw|

35. anonymous

What is Latex?

36. jim_thompson5910

it's a tool to help write math notation

37. anonymous

Oh...

38. 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|

39. jim_thompson5910

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

40. 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

41. 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?

42. jim_thompson5910

I'm not sure what you mean

43. jim_thompson5910

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

44. 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?

45. 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)

46. jim_thompson5910

|dw:1441239084919:dw|

47. jim_thompson5910

|dw:1441239111134:dw|

48. jim_thompson5910

|dw:1441239138986:dw|

49. anonymous

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

50. anonymous

|dw:1441238954330:dw|

51. anonymous

Sorry the drawing board was malfunctioning

52. anonymous

It's suppose to be a straight line

53. 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|

54. anonymous

Ohh ya! I forgot about that.

55. 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|

56. jim_thompson5910

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

57. anonymous

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

58. jim_thompson5910

you're welcome