Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathcalculus Group Title

@asnaseer finding the limit:

  • one year ago
  • one year ago

  • This Question is Closed
  1. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    • one year ago
    1 Attachment
  2. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    have you attempted to sketch the curve first?

    • one year ago
  3. FutureMathProfessor Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1375034315072:dw|

    • one year ago
  4. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    which part are you stuck on?

    • one year ago
  5. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    how do i sketch if i dont know the points

    • one year ago
  6. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    all i see are x+1, x <> 2 then im stuck

    • one year ago
  7. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i can't use calculator.

    • one year ago
  8. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok - lets break it down into smaller steps

    • one year ago
  9. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    first, you are told that:\[f(x)=x+1\]if \(x\le2\) agreed?

    • one year ago
  10. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

    • one year ago
  11. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so lets sketch this...

    • one year ago
  12. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so for a) since it;s coming from the left side it must be negative... and we use the top function, correct?

    • one year ago
  13. FutureMathProfessor Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Its already been sketched btw

    • one year ago
  14. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375034583963:dw|

    • one year ago
  15. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok how did you sketch that ? :(

    • one year ago
  16. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I just sketched y=x+1 got 2 points on it: when x=0, y=1 when x=2, y=3 and then just drew a line

    • one year ago
  17. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    we are told that this is only for x less than or equal to 2. so we need to CHOP the curve at x=2 and draw a filled-in dot at that point. it needs to be filled-in because it INCLUDES the value at x=2

    • one year ago
  18. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so the actual line should look like this:

    • one year ago
  19. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    does that make sense?

    • one year ago
  20. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ohhhhh okay :)

    • one year ago
  21. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375034970995:dw|

    • one year ago
  22. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so when are the times that we fill in the dots?

    • one year ago
  23. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and don't fill in?

    • one year ago
  24. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you always fill-in the dots if the point INCLUDES the value - so all these would result in filling in the dot:\[x\le2\]\[x=2\]\[x\ge2\]and all these would NOT be filled-in:\[x<2\]\[x>2\]

    • one year ago
  25. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    note that the first 3 INCLUDE the point x=2

    • one year ago
  26. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    if that makes sense, then we can move onto the next part...

    • one year ago
  27. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ?

    • one year ago
  28. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes :)

    • one year ago
  29. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so stoping at two we fill in

    • one year ago
  30. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

    • one year ago
  31. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and whatever is greater than 2 we leave alone?

    • one year ago
  32. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i got it..

    • one year ago
  33. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, so 2nd part of the curve is defined as:\[f(x)=1\]if \(x\gt2\) agreed?

    • one year ago
  34. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

    • one year ago
  35. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so first lets sketch f(x) = 1

    • one year ago
  36. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375035727853:dw|

    • one year ago
  37. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    wait, can't we sketch x=3 because it says x is GREATER than 2

    • one year ago
  38. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    now here we are told that this part is only valid for \(x\gt2\), so we need to draw a circle (not filled-in) at the point x=2 and throw away everything to the left of this point

    • one year ago
  39. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375035852984:dw|

    • one year ago
  40. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah but wait, im not sure why we are using 1 when we can use 3 since it says x>2

    • one year ago
  41. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the value of f(x) = 1 for x greater than 2

    • one year ago
  42. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    that includes points such as x=2.000001, x=2.5, x=3, x=99, etc

    • one year ago
  43. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i.e. ALL points to the right of (and NOT including) x=2

    • one year ago
  44. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375035980350:dw|

    • one year ago
  45. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh okay so i can use 3.. great

    • one year ago
  46. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so now we just combine both parts of the curve to get...

    • one year ago
  47. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375036030210:dw|

    • one year ago
  48. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    make sense?

    • one year ago
  49. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375036145535:dw|

    • one year ago
  50. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    got it

    • one year ago
  51. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    good. now we can examine the lmits

    • one year ago
  52. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok :)

    • one year ago
  53. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the 1st one is limit as x tends to 2 from the negative side

    • one year ago
  54. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so - look at the curves and see what you think the answer should be for this case

    • one year ago
  55. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375036264164:dw|

    • one year ago
  56. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    1 zt 2^-

    • one year ago
  57. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    at*

    • one year ago
  58. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    why is it -1 and not 1?

    • one year ago
  59. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ?

    • one year ago
  60. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i see it's coming from the left side and the answer is going to be negative.

    • one year ago
  61. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    why is it going to be negative?

    • one year ago
  62. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    but where do i look, in the y?

    • one year ago
  63. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    because it's coming from the left?

    • one year ago
  64. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    lets approach the limit in steps

    • one year ago
  65. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    how do i look for the limit when it approaches to 2?

    • one year ago
  66. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375036393036:dw|

    • one year ago
  67. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1375036417600:dw|

    • one year ago
  68. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    can you see now what the limit should be as x approaches 2 from the left-hand-side?

    • one year ago
  69. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so its 3?

    • one year ago
  70. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    perfect! well done! :)

    • one year ago
  71. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    now try to do the same for x approaching 2 from the right-hand-side

    • one year ago
  72. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    right side of 2 it approaches at 1

    • one year ago
  73. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    bingo! you're a pro now! :)

    • one year ago
  74. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    2 is undefined?

    • one year ago
  75. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the /tricky/ part now is what is the limit as x approaches 2 (without being told whether its from the left or right side)?

    • one year ago
  76. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes!

    • one year ago
  77. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I believe you have grokked this now! :)

    • one year ago
  78. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    because, it's not coming from either side.

    • one year ago
  79. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    omg thank you!!!! :))

    • one year ago
  80. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you so much!!

    • one year ago
  81. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yw - I'm glad I was to explain it well enough for you to understand. :)

    • one year ago
  82. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    i'll apply this to the rest when im doing a problem

    • one year ago
  83. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    perfect! - keep at it - you seem to have a natural ability at this. :)

    • one year ago
  84. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What if they tell us to calculate instead of sketching?

    • one year ago
  85. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    do we simply substitute?

    • one year ago
  86. mathcalculus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @asnaseer

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.