## schmidtdancer Group Title FIND the limit!! 2 years ago 2 years ago

1. schmidtdancer Group Title

|dw:1343661876978:dw|

2. agentx5 Group Title

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

3. schmidtdancer Group Title

ok

4. ParthKohli Group Title

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

5. ParthKohli Group Title

Let's see how the graph is..

6. schmidtdancer Group Title

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

7. ParthKohli Group Title

Don't do that now.

8. agentx5 Group Title

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

9. ParthKohli Group Title

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

10. schmidtdancer Group Title

Ok

11. ParthKohli Group Title

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

12. agentx5 Group Title

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 Group Title

ok! can you show how I would solve it

14. schmidtdancer Group Title

Ok i understand that

15. telliott99 Group Title

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

16. schmidtdancer Group Title

So how would I solve the limit?

17. ParthKohli Group Title

By plugging numbers slightly less than 3.

18. agentx5 Group Title

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

19. telliott99 Group Title

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

20. schmidtdancer Group Title

2.99(9-2.99^2)

21. ParthKohli Group Title

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

22. schmidtdancer Group Title

for 2.5, f(x) would be 4.145

23. ParthKohli Group Title

Find them for all.

24. agentx5 Group Title

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 Group Title

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 Group Title

Calculator, Schmidt.

27. schmidtdancer Group Title

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

28. agentx5 Group Title

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

29. schmidtdancer Group Title

I got 7.3484

30. ParthKohli Group Title

Just not 3.

31. ParthKohli Group Title

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

32. schmidtdancer Group Title

Ok! I think its going to be 7.5

33. ParthKohli Group Title

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

34. schmidtdancer Group Title

I just tried for that

35. schmidtdancer Group Title

can someone tell me if im right

36. ParthKohli Group Title

I am too lazy to do so :/

37. schmidtdancer Group Title

come onnn lol

38. schmidtdancer Group Title

plz! i really need your help..

39. ParthKohli Group Title

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

40. schmidtdancer Group Title

OK

41. ParthKohli Group Title

@agentx5 Where is the graph?

42. agentx5 Group Title

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 Group Title

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

44. ParthKohli Group Title

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

45. ParthKohli Group Title

The limit was getting smaller and smaller. ;)

46. ParthKohli Group Title

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

47. ParthKohli Group Title

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

48. agentx5 Group Title

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

49. schmidtdancer Group Title

like 2 or 3 right?

50. agentx5 Group Title

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 Group Title

Guys do you know the actual limit?

52. agentx5 Group Title

Yes.

53. agentx5 Group Title

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

54. schmidtdancer Group Title

Yeah I do see it visually,

55. schmidtdancer Group Title

is the limit around 2 or 3

56. schmidtdancer Group Title

wait it looks around 0

57. agentx5 Group Title

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

58. schmidtdancer Group Title

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

59. schmidtdancer Group Title

sorry i meant, as x approaches 3

60. agentx5 Group Title

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 Group Title

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

62. agentx5 Group Title

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 Group Title

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

64. agentx5 Group Title

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 Group Title

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

66. agentx5 Group Title

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

67. agentx5 Group Title

You will see DNE problems, I can guarantee you.

68. schmidtdancer Group Title

Oh yeah, I know!:)