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Jaweria

  • 2 years ago

I need help with one question of Calculus 1.

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  1. dave0616
    • 2 years ago
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    what is your question?

  2. Jaweria
    • 2 years 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
    • 2 years ago
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    And also tell whether your estimate is an over or an upper estimate, explain why?

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

  5. Jaweria
    • 2 years ago
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    ok thx

  6. Jaweria
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    yeah

  9. Jaweria
    • 2 years ago
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    but can you please check my numbers plzz

  10. dave0616
    • 2 years 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
    • 2 years 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
    • 2 years ago
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    so whats my answer basically?

  13. Jaweria
    • 2 years ago
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    Someone plzz help me

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

  15. dave0616
    • 2 years 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
    • 2 years ago
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    i thought its over estimate because its increasing

  17. dave0616
    • 2 years 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
    • 2 years ago
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    oh thx

  19. dave0616
    • 2 years ago
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    no problem

  20. Jaweria
    • 2 years ago
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    one more plzz

  21. dave0616
    • 2 years ago
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    shoot

  22. Jaweria
    • 2 years ago
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    if you dont mind

  23. Jaweria
    • 2 years ago
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    ok

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

  25. Jaweria
    • 2 years ago
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    from 1<equal to x <equalt to 6

  26. Jaweria
    • 2 years ago
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    |dw:1366349539104:dw|

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

  28. Jaweria
    • 2 years ago
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    its ok

  29. Jaweria
    • 2 years ago
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    so how am I actually going to solve this

  30. dave0616
    • 2 years ago
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    are you supposed to use 5 boxes again?

  31. Jaweria
    • 2 years ago
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    yeah its says 5 rectangles

  32. dave0616
    • 2 years 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
    • 2 years ago
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    yeah

  34. Jaweria
    • 2 years ago
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    and it also gives you from where to where

  35. Jaweria
    • 2 years ago
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    which is this |dw:1366349945211:dw|

  36. dave0616
    • 2 years 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
    • 2 years ago
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    ok

  38. Jaweria
    • 2 years ago
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    can we work on this together little bit ?

  39. Jaweria
    • 2 years ago
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    If you dont mind?

  40. dave0616
    • 2 years 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
    • 2 years ago
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    can you first show me how to get the value for the 1st rectangle?

  42. dave0616
    • 2 years 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
    • 2 years ago
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    @Jaweria

  44. Jaweria
    • 2 years ago
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    hand

  45. Jaweria
    • 2 years ago
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    we are not allow to use calculator

  46. dave0616
    • 2 years 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
    • 2 years ago
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    ok so first I m using 1 for my y

  48. dave0616
    • 2 years 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
    • 2 years ago
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    oh ok

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

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

  52. Jaweria
    • 2 years ago
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    alright

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

  54. dave0616
    • 2 years ago
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    did you get the values?

  55. Jaweria
    • 2 years ago
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    so far I got 10,4,0

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

  57. Jaweria
    • 2 years ago
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    ok

  58. Jaweria
    • 2 years ago
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    its 0

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

  60. Jaweria
    • 2 years ago
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    ok

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

  62. dave0616
    • 2 years ago
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    @jaweria

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

  64. dave0616
    • 2 years ago
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    its all good no worries

  65. Jaweria
    • 2 years ago
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    I got -10

  66. Jaweria
    • 2 years ago
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    is that right?

  67. dave0616
    • 2 years 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
    • 2 years ago
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    I got -6 for 4

  69. Jaweria
    • 2 years ago
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    and -8 for 5

  70. dave0616
    • 2 years 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
    • 2 years ago
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    so A=0+4+0-6-8. what do you get for area?

  72. Jaweria
    • 2 years ago
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    yeah i got that too all of them

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

  74. Jaweria
    • 2 years ago
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    and then divide it by some number?

  75. dave0616
    • 2 years 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
    • 2 years ago
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    can you solve for area from that?

  77. Jaweria
    • 2 years ago
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    oh ok

  78. dave0616
    • 2 years ago
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    what do you get for area?

  79. Jaweria
    • 2 years ago
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    yeah its -10

  80. Jaweria
    • 2 years ago
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    I m still getting -10

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

  82. Jaweria
    • 2 years ago
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    yup

  83. dave0616
    • 2 years 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
    • 2 years ago
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    its ok :)

  85. Jaweria
    • 2 years ago
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    so thats my answer ?

  86. dave0616
    • 2 years 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
    • 2 years ago
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    yup I completely did thanks a lot:)

  88. dave0616
    • 2 years ago
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    absolutely no problem!

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

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

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