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Jaweria

  • one year ago

I need help with one question of Calculus 1.

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  1. dave0616
    • one year ago
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    what is your question?

  2. Jaweria
    • one year ago
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    My question is this: USe 5 rectangles to estimate the area under the graph of: f(x) = 2x^3+2x-5. from x=2 to x=7

  3. Jaweria
    • one year ago
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    And also tell whether your estimate is an over or an upper estimate, explain why?

  4. dave0616
    • one year ago
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    oh you are doing reimann sums? let me do some work, give me a second

  5. Jaweria
    • one year ago
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    ok thx

  6. Jaweria
    • one year ago
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    if you can check with me that I got my 5 rectangles: 35, 93, 193, -92, -128 are they right?

  7. dave0616
    • one year ago
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    hmmmmm im gonna draw up the graph so that we know we have the same thing|dw:1366346945142:dw| That is the graph that i have, roughly at least, is that the same thing that you are working with?

  8. Jaweria
    • one year ago
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    yeah

  9. Jaweria
    • one year ago
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    but can you please check my numbers plzz

  10. dave0616
    • one year ago
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    i punched this into my calculator, and the base for each rectangle would be 1, because you are using 5 rectangles, and the difference between 7 and 2 is 5. so you are basicallly looking at the height, but i got 15, 55, 131, 255, and 439. i dont see how you could get any negative because the line is going up

  11. Jaweria
    • one year ago
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    yeah i got that too but I m saying that arent we suppose to add up those rectangles?

  12. Jaweria
    • one year ago
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    so whats my answer basically?

  13. Jaweria
    • one year ago
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    Someone plzz help me

  14. jojo921
    • one year ago
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    intervals =b-a/n (7-2)/5 =1

  15. dave0616
    • one year ago
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    yea, you just add what you got for the areas, so 15+55+131+255+439=839. and it would be an under estimate because it is a left side reimann sum. meaning that the left corner of the boxes hit the line

  16. Jaweria
    • one year ago
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    i thought its over estimate because its increasing

  17. dave0616
    • one year ago
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    |dw:1366348904077:dw| that isnt to scale, but that is the basic idea of what is going on

  18. Jaweria
    • one year ago
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    oh thx

  19. dave0616
    • one year ago
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    no problem

  20. Jaweria
    • one year ago
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    one more plzz

  21. dave0616
    • one year ago
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    shoot

  22. Jaweria
    • one year ago
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    if you dont mind

  23. Jaweria
    • one year ago
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    ok

  24. Jaweria
    • one year ago
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    Use 5 rectangles to esitmate the area under the graph: y=x^3-10x^2+27x-18

  25. Jaweria
    • one year ago
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    from 1<equal to x <equalt to 6

  26. Jaweria
    • one year ago
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    |dw:1366349539104:dw|

  27. dave0616
    • one year ago
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    ok so your graph is going to look like: |dw:1366349701319:dw| roughly of course.

  28. Jaweria
    • one year ago
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    its ok

  29. Jaweria
    • one year ago
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    so how am I actually going to solve this

  30. dave0616
    • one year ago
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    are you supposed to use 5 boxes again?

  31. Jaweria
    • one year ago
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    yeah its says 5 rectangles

  32. dave0616
    • one year ago
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    does this problem have the same basis as the other problem you posted? meaning you are just looking for rectangles to find the area under the graph? ok, 5 rectangles

  33. Jaweria
    • one year ago
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    yeah

  34. Jaweria
    • one year ago
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    and it also gives you from where to where

  35. Jaweria
    • one year ago
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    which is this |dw:1366349945211:dw|

  36. dave0616
    • one year ago
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    right, so this again is the same difference as the other problem, (5) so each will have the same base length of 1

  37. Jaweria
    • one year ago
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    ok

  38. Jaweria
    • one year ago
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    can we work on this together little bit ?

  39. Jaweria
    • one year ago
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    If you dont mind?

  40. dave0616
    • one year ago
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    yes of course we can. how would you like to do that? i would like to help you in the best way that suits you

  41. Jaweria
    • one year ago
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    can you first show me how to get the value for the 1st rectangle?

  42. dave0616
    • one year ago
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    yes, i personally am using a graphing calculator because i find it is the easiest way to do it. are you using the same, or are you trying to do this by hand?

  43. dave0616
    • one year ago
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    @Jaweria

  44. Jaweria
    • one year ago
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    hand

  45. Jaweria
    • one year ago
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    we are not allow to use calculator

  46. dave0616
    • one year ago
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    ok, that is fine, that just means that we are going to have to find the value for y at every point. and our points are going to be 1,2,3,4,5,6. do you think you can solve for y using the equation for these six points? and would you like to solve them on your own, and then post them, and we can compare values?

  47. Jaweria
    • one year ago
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    ok so first I m using 1 for my y

  48. dave0616
    • one year ago
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    nope, we are gonna be solving for y, so we are going to plug 1,2,3,4,5 and 6 in for x into the equation

  49. Jaweria
    • one year ago
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    oh ok

  50. dave0616
    • one year ago
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    so solve for y, using those six values and let me know what you get

  51. Jaweria
    • one year ago
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    so let me get their values then I ll tell you

  52. Jaweria
    • one year ago
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    alright

  53. dave0616
    • one year ago
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    ok, and solve for 1,2,3,4,5 that will give us 5 rectangles

  54. dave0616
    • one year ago
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    did you get the values?

  55. Jaweria
    • one year ago
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    so far I got 10,4,0

  56. dave0616
    • one year ago
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    hmmmm, that first one isnt correct try it again

  57. Jaweria
    • one year ago
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    ok

  58. Jaweria
    • one year ago
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    its 0

  59. dave0616
    • one year ago
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    that is correct, now go ahead and fine the y value for 4 and 5

  60. Jaweria
    • one year ago
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    ok

  61. dave0616
    • one year ago
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    did you solve for them? sorry if i am rushing you, i dont mean to be

  62. dave0616
    • one year ago
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    @jaweria

  63. Jaweria
    • one year ago
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    I m sorry my stupid laptop is giving me tough time

  64. dave0616
    • one year ago
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    its all good no worries

  65. Jaweria
    • one year ago
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    I got -10

  66. Jaweria
    • one year ago
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    is that right?

  67. dave0616
    • one year ago
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    you need, two more values, but -10 is not correct, you are going to need to solve for 4 and 5. go ahead and do that and let me know what you get

  68. Jaweria
    • one year ago
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    I got -6 for 4

  69. Jaweria
    • one year ago
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    and -8 for 5

  70. dave0616
    • one year ago
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    that is correct. now we need to find the area of each of those rectangles. and the base of each of those rectangles is 1, so the area of each of those rectangles will be equal to the value, so we have 0,4,0,-6,-8. so now all we need to do is add those values.

  71. dave0616
    • one year ago
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    so A=0+4+0-6-8. what do you get for area?

  72. Jaweria
    • one year ago
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    yeah i got that too all of them

  73. Jaweria
    • one year ago
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    but then how am i suppose to find an area add them up?

  74. Jaweria
    • one year ago
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    and then divide it by some number?

  75. dave0616
    • one year ago
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    we found that the base of each of those rectangles would be 1. and the area of a rectangle is b*h. we found the height by finding the y. so in essence you are multplying each of the values we found (0,4,0,-6,-8) by one, but they will equal the values themselves. so what wer are actually doing is A=0(1)+4(1)+0(1)-6(1)-8(1)

  76. dave0616
    • one year ago
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    can you solve for area from that?

  77. Jaweria
    • one year ago
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    oh ok

  78. dave0616
    • one year ago
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    what do you get for area?

  79. Jaweria
    • one year ago
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    yeah its -10

  80. Jaweria
    • one year ago
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    I m still getting -10

  81. dave0616
    • one year ago
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    thta is right. is that what you were reffering to earlier when you said -10?

  82. Jaweria
    • one year ago
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    yup

  83. dave0616
    • one year ago
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    oh im extremely sorry, i did not realize that is what you were referrring to. i really do feel bad, im sorry. but yes it is -10, and it would still be an under estimate because we used a left corner triangle

  84. Jaweria
    • one year ago
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    its ok :)

  85. Jaweria
    • one year ago
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    so thats my answer ?

  86. dave0616
    • one year ago
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    haha ok. well im glad we went through it still. yes the area under the graph by the estimate of 5 rectangles is -10. do you understand how we came to the answer?

  87. Jaweria
    • one year ago
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    yup I completely did thanks a lot:)

  88. dave0616
    • one year ago
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    absolutely no problem!

  89. Jaweria
    • one year ago
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    I should go to sleep now its really late take care bye.

  90. dave0616
    • one year ago
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    i hear ya haha. take care and good luck in your studies

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