## schmidtdancer 3 years ago FIND the limit!!

1. schmidtdancer

|dw:1343661876978:dw|

2. agentx5

Ah! This is one best though of visually, let me make you a graph:

3. schmidtdancer

ok

4. ParthKohli

If you find the function continuous, then you may just plug 3 for $$x$$ by the way.

5. ParthKohli

Let's see how the graph is..

6. schmidtdancer

Ok. If I plug in 3, I get 3 sqrt(0)

7. ParthKohli

Don't do that now.

8. agentx5

What you need are numbers slightly less than 3, like 2.9999999999999

9. ParthKohli

Looks like we can plug in values less than $$3$$.

10. schmidtdancer

Ok

11. ParthKohli

Because it is a left handed limit, we may plug numbers like agentx5 said :)

12. agentx5

That - sign above the limit means "numbers from the left hand side limit" or the number slightly less than 3 (but as close as you can get)

13. schmidtdancer

ok! can you show how I would solve it

14. schmidtdancer

Ok i understand that

15. telliott99

About your graph, notice what happens to the function for x > 3

16. schmidtdancer

So how would I solve the limit?

17. ParthKohli

By plugging numbers slightly less than 3.

18. agentx5

@telliott99 , I know... look at the notation for imaginary and real...

19. telliott99

Just saying the graph is not correct. It doesn't have a hole in it. And do what @ParthKohli says

20. schmidtdancer

2.99(9-2.99^2)

21. ParthKohli

$\begin{array}{l|r} x & f(x) \\ \hline 2.5 & \\ 2.9 \\ 2.999 \\ 2.99999\end{array}$ Fill the f(x)'s.

22. schmidtdancer

for 2.5, f(x) would be 4.145

23. ParthKohli

Find them for all.

24. agentx5

And and as you get closer and closer to 2.999999999999? Every closer to 3 from the "just under" side and you'll approach some limit.

25. schmidtdancer

Ok can you help find the limit now? Like I understand how to find that, i just dont haeve time to find them all

26. ParthKohli

Calculator, Schmidt.

27. schmidtdancer

so agentx5, I should just use 2.999999 to find the limit?

28. agentx5

Or if you prefer, 2.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999... Get the point? :P

29. schmidtdancer

I got 7.3484

30. ParthKohli

Just not 3.

31. ParthKohli

Looks like its getting closer to 7.5, but let's see it for more values.

32. schmidtdancer

Ok! I think its going to be 7.5

33. ParthKohli

Are you sure? Try for 2.9999999 and 2.999999999999999. So on.

34. schmidtdancer

I just tried for that

35. schmidtdancer

can someone tell me if im right

36. ParthKohli

I am too lazy to do so :/

37. schmidtdancer

come onnn lol

38. schmidtdancer

plz! i really need your help..

39. ParthKohli

All right :) let me check it out on Wolfram.

40. schmidtdancer

OK

41. ParthKohli

@agentx5 Where is the graph?

42. agentx5

Here's the algebra trick, you need to find what y would be when x=3. You can't do this normally but... $$x\sqrt{(3+x)(3-x)}$$ , For what solutions does y = 0? Well, 0, +3 and -3. So... ;-) Replacing with a better graph (more accurate, real #'s only): |dw:1343662913297:dw|

43. schmidtdancer

ok thx @agentx5 so what would the limit be for this probb?

44. ParthKohli

I was actually surprised how I was plugging values and getting it approaching something else. Hence, I asked.

45. ParthKohli

The limit was getting smaller and smaller. ;)

46. ParthKohli

You may find from the graph, actually.|dw:1343663313029:dw|

47. ParthKohli

What is $$y$$ approaching in the graph? ^

48. agentx5

With the limit shown... |dw:1343663226621:dw|

49. schmidtdancer

like 2 or 3 right?

50. agentx5

I actually had my imaginary lines going the wrong way @telliott99 and the circles were too high in the original sketch (they're on the x-axis), I stand corrected. Although I'm not sure that's what you meant. ;-)

51. schmidtdancer

Guys do you know the actual limit?

52. agentx5

Yes.

53. agentx5

And I'm trying to help you learn visually what's going on so you're not lost here

54. schmidtdancer

Yeah I do see it visually,

55. schmidtdancer

is the limit around 2 or 3

56. schmidtdancer

wait it looks around 0

57. agentx5

$\lim_{x \rightarrow 3^-}$ What is the output of the function approaching? The input gets closer to 3 from the "slightly less" side.

58. schmidtdancer

as 3 approaches 3 from the left, the y value is 0, right?

59. schmidtdancer

sorry i meant, as x approaches 3

60. agentx5

Or using the analytical method, as you plug in larger and larger 2.9999999999999999...'s you get smaller and smaller numbers. Infinitesimally small. To the point gets damned close to zero. Thus the limit is zero, correct.

61. schmidtdancer

ok so the limit for this function is 0? :D

62. agentx5

The reason you can't just substitute 3 in place of x, officially is because you might have one like this: $\lim_{x \rightarrow 1} = \frac{1}{1-x}$ Look what happens if you plug in 1?

63. schmidtdancer

But, limit is 0 right? and yes the ddenominator bneomes 0.. not possible

64. agentx5

In this case your left and your right hand limits are going in opposite directions, and the limit doesn't exist. |dw:1343663845294:dw| And yes, twice to the above post. :-)

65. schmidtdancer

wait so the limit is DNE? or zero!?!

66. agentx5

For your original problem, Zero. For the one I just asked you, trying to get you to learn, Does Not Exist.

67. agentx5

You will see DNE problems, I can guarantee you.

68. schmidtdancer

Oh yeah, I know!:)