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AravindG Group Title

Please help: can u explain detailed what is a tangent to a curve .I know its a line just touching the curve at only one point but i need to understand it more and also would like to know how to draw the tangent if i am given any graph .Is THERE ONLY ONE tangent possible at a point?

  • 2 years ago
  • 2 years ago

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  1. UnkleRhaukus Group Title
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    |dw:1346418663569:dw|

    • 2 years ago
  2. AravindG Group Title
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    @Callisto , @.Sam. , @eliassaab , @lgbasallote , @satellite73 , @mukushla

    • 2 years ago
  3. Mikael Group Title
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    In the general case the slope is computed by derivative. But for circles - the straight line is PERPENDICULAR to the radius at the point of tangent

    • 2 years ago
  4. UnkleRhaukus Group Title
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    |dw:1346418733121:dw|

    • 2 years ago
  5. AravindG Group Title
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    i knw about tangent in circles ..my prob is i dont get idea on tangents of curves

    • 2 years ago
  6. AravindG Group Title
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    i cant draw tangent at a point if i am given a figure

    • 2 years ago
  7. UnkleRhaukus Group Title
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    |dw:1346418814483:dw|

    • 2 years ago
  8. AravindG Group Title
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    |dw:1346418865060:dw|

    • 2 years ago
  9. UnkleRhaukus Group Title
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    |dw:1346418835881:dw|

    • 2 years ago
  10. AravindG Group Title
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    perpendicular to what?

    • 2 years ago
  11. AravindG Group Title
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    |dw:1346418935365:dw| what is tangent at P?

    • 2 years ago
  12. Mikael Group Title
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    Aravind - where the curve itself is flat (straight) the tangent coincides with it.

    • 2 years ago
  13. AravindG Group Title
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    @Mikael WHY???

    • 2 years ago
  14. Mikael Group Title
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    |dw:1346418660977:dw|

    • 2 years ago
  15. AravindG Group Title
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    if it is coincidnt it will touch at more than one point!!

    • 2 years ago
  16. Mikael Group Title
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    Because the tangent to a straight i this straight line !

    • 2 years ago
  17. AravindG Group Title
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    but tangent is defined to touch only at a point...err i am confused

    • 2 years ago
  18. Mikael Group Title
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    Yes it will "touch" at infinitely many points

    • 2 years ago
  19. amishra Group Title
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    A tangent is a line outside the circle which touches only one point of the circle. Through one given point, infinite tangents can be drawn. A tangent at a given point is perpendicular to the radius of the circle.

    • 2 years ago
  20. UnkleRhaukus Group Title
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    yes , @Mikael the tangent is the flat line approximation of the curve

    • 2 years ago
  21. AravindG Group Title
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    Through one given point in a curve, infinite tangents can be drawn. "is that true?

    • 2 years ago
  22. Mikael Group Title
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    No, no no

    • 2 years ago
  23. AravindG Group Title
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    only one ryt?

    • 2 years ago
  24. Mikael Group Title
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    Almost - two

    • 2 years ago
  25. AravindG Group Title
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    ????

    • 2 years ago
  26. Mikael Group Title
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    |dw:1346418836231:dw|

    • 2 years ago
  27. AravindG Group Title
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    @Mikael read the qn agian Through one given point in a curve, infinite tangents can be drawn. "is that true?

    • 2 years ago
  28. AravindG Group Title
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    Through ONE given point in a curve, infinite tangents can be drawn. "is that true?

    • 2 years ago
  29. Mikael Group Title
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    Read what @UnkleRhaukus said: this is the full definition: flat approximation

    • 2 years ago
  30. AravindG Group Title
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    i think the answer is 1

    • 2 years ago
  31. Mikael Group Title
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    No - just one single well-defined tangent

    • 2 years ago
  32. AravindG Group Title
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    yep :) only one tangent is allowed at point ryt?

    • 2 years ago
  33. UnkleRhaukus Group Title
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    i can not think of any example where a curve could have more than one tangent

    • 2 years ago
  34. Mikael Group Title
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    At point ON the curve YES "there can be only one" As Duncan McCloud says

    • 2 years ago
  35. AravindG Group Title
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    @UnkleRhaukus i liked ur definition the tangent is the flat line approximation of the curve

    • 2 years ago
  36. Mikael Group Title
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    It is not his (he would be lucky to be Isaac Newton, but he is unfortunately NOT)

    • 2 years ago
  37. AravindG Group Title
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    those are newtons words??

    • 2 years ago
  38. UnkleRhaukus Group Title
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    it's not mine you say?

    • 2 years ago
  39. AravindG Group Title
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    @UnkleRhaukus ?

    • 2 years ago
  40. Mikael Group Title
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    I say that "tangent is a flat approximation to the curve" is ORIGINALLY Newton's definition.

    • 2 years ago
  41. UnkleRhaukus Group Title
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    wow, where can i see that?

    • 2 years ago
  42. AravindG Group Title
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    "GREAT MINDS THINK ALIKE "

    • 2 years ago
  43. Mikael Group Title
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    "Principia Mathematicae" (National Library, also the Library of the British Academy of Sciences

    • 2 years ago
  44. Mikael Group Title
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    Sorry - The Royal Academy od Sciences

    • 2 years ago
  45. UnkleRhaukus Group Title
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    we i havent read that one, ( i think its in latin)

    • 2 years ago
  46. Mikael Group Title
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    I can get you a recent English Translation by a nobel prize winner (countrymanof Aravind originally...)

    • 2 years ago
  47. AravindG Group Title
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    HMM..CAN u guys give me some real life situations where calculation of tangents is necessary?

    • 2 years ago
  48. Mikael Group Title
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    @UnkleRhaukus for a small fee naturally >;]

    • 2 years ago
  49. Mikael Group Title
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    Yeah , Let\[f(x) = 33x^2 + 18x - 15\] Find the tangent to this curve whose slope equals 99

    • 2 years ago
  50. AravindG Group Title
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    @Mikael i mean not that way

    • 2 years ago
  51. UnkleRhaukus Group Title
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    The only example i can think of where you could have multiple tangents is if they had som scale associated with them |dw:1346419654145:dw|

    • 2 years ago
  52. AravindG Group Title
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    well i need real life example where calculation of tangent is necessary

    • 2 years ago
  53. AravindG Group Title
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    for eg.space vehicle trajectory after it leaves earth

    • 2 years ago
  54. Mikael Group Title
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    Yes this is very much related to original problems Newton had to solve - instantaneous velocity

    • 2 years ago
  55. AravindG Group Title
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    more examples?

    • 2 years ago
  56. Mikael Group Title
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    • 2 years ago
    1 Attachment
  57. UnkleRhaukus Group Title
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    |dw:1346419864709:dw|

    • 2 years ago
  58. Mikael Group Title
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    Well - suppose Mr. Buffet has 23*10^9 $ in a hedge fund. Assume that his interest accumulates at 1% per second, draw the linear graph (straight line) approximating his wealth grouth after 27 seconds

    • 2 years ago
  59. Mikael Group Title
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    This will be solved by a tangent to exponential function graph

    • 2 years ago
  60. AravindG Group Title
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    @UnkleRhaukus nic pic :P

    • 2 years ago
  61. AravindG Group Title
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    @Mikael do u have more?

    • 2 years ago
  62. UnkleRhaukus Group Title
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    does it look like some athlete throwing a hammer ?

    • 2 years ago
  63. AravindG Group Title
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    i thought someone was spinning thee bucket :P

    • 2 years ago
  64. Mikael Group Title
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    Yes - the typical (boring) school/colledge example would be:

    • 2 years ago
  65. UnkleRhaukus Group Title
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    instantaneous velocity or speed is the tangent of distance/time

    • 2 years ago
  66. Mikael Group Title
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    Let f(x) = (45x^2 -33x + 7) sin (x-5) . Find the approximate value at 5.01 using the linear approximation with its slope = derivative at x=5

    • 2 years ago
  67. Mikael Group Title
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    Btw @UnkleRhaukus did u open the picture I have attached above ?

    • 2 years ago
  68. AravindG Group Title
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    One last question which i gt stuck today : Find the equation of the tangent to the curve y=x-7/((x-2)(x-3)) at the point where it cuts the x axis.

    • 2 years ago
  69. UnkleRhaukus Group Title
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    looks like 150$ i dont have @Mikael

    • 2 years ago
  70. AravindG Group Title
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    help please

    • 2 years ago
  71. Mikael Group Title
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    Let's show you the general idea to Find the equation of the tangent to the curve y=f(x) at the point x1

    • 2 years ago
  72. AravindG Group Title
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    \[y=\frac{(x-7)}{(x-2)(x-3)}\]

    • 2 years ago
  73. Mikael Group Title
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    1. Find the point (in ur case the intersection with the axis)

    • 2 years ago
  74. AravindG Group Title
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    @Mikael i knw dat i done so many problems

    • 2 years ago
  75. Mikael Group Title
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    2 Derivative at that point

    • 2 years ago
  76. AravindG Group Title
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    i cannot differentiate this coorectly

    • 2 years ago
  77. AravindG Group Title
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    i tred logarithmic differentiation

    • 2 years ago
  78. AravindG Group Title
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    nt getting

    • 2 years ago
  79. Mikael Group Title
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    Now you have THREE ( 3 ) data: (x, f(x)) and the slope=derivative

    • 2 years ago
  80. AravindG Group Title
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    help please

    • 2 years ago
  81. Mikael Group Title
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    Hey what the fuss it is simple Ratio function

    • 2 years ago
  82. AravindG Group Title
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    i did like this

    • 2 years ago
  83. AravindG Group Title
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    |dw:1346420490258:dw|

    • 2 years ago
  84. Mikael Group Title
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    \[(\frac{ f }{ g }) = \frac{ f'*g - f*g'}{ g^2}\]

    • 2 years ago
  85. AravindG Group Title
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    now when i put in x=7 i am stuck

    • 2 years ago
  86. Mikael Group Title
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    You did fine (beginning at least)

    • 2 years ago
  87. Mikael Group Title
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    Then do the formula above

    • 2 years ago
  88. AravindG Group Title
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    i think using quotient rule complicates the answer

    • 2 years ago
  89. AravindG Group Title
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    what is wrong with my working

    • 2 years ago
  90. Mikael Group Title
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    Yes , but it GETS YOU THERE

    • 2 years ago
  91. AravindG Group Title
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    @UnkleRhaukus sharre ur view

    • 2 years ago
  92. AravindG Group Title
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    my text says another method :

    • 2 years ago
  93. Mikael Group Title
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    Which is ...?

    • 2 years ago
  94. AravindG Group Title
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    |dw:1346420702829:dw|

    • 2 years ago
  95. AravindG Group Title
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    i they havent shown how they gt it :(

    • 2 years ago
  96. AravindG Group Title
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    @Mimi can u help?

    • 2 years ago
  97. Mikael Group Title
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    WHAAT the f. ??? How did y get there - in the denumer ?

    • 2 years ago
  98. AravindG Group Title
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    ya i am also puzzled

    • 2 years ago
  99. AravindG Group Title
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    @Mimi_x3

    • 2 years ago
  100. Mikael Group Title
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    Why not use simple and direct Ratio deriv. formula ??!

    • 2 years ago
  101. AravindG Group Title
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    i dont knw can u fig out what the text has used ?

    • 2 years ago
  102. AravindG Group Title
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    @ash2326 , @myininaya PLS HELP

    • 2 years ago
  103. Mikael Group Title
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    Yes - Now i understand

    • 2 years ago
  104. AravindG Group Title
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    HOW?

    • 2 years ago
  105. Mikael Group Title
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    Stop - you will awake all the evil spirits. It is a simple trick

    • 2 years ago
  106. AravindG Group Title
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    ?

    • 2 years ago
  107. Mikael Group Title
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    Lets start:

    • 2 years ago
  108. AravindG Group Title
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    go on

    • 2 years ago
  109. Mikael Group Title
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    When one applies the ratio formula one gets

    • 2 years ago
  110. UnkleRhaukus Group Title
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    .

    • 2 years ago
  111. Mikael Group Title
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    \[\frac{ Polynom }{ ((x-2)(x-3))^2}\]

    • 2 years ago
  112. AravindG Group Title
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    so?

    • 2 years ago
  113. Mikael Group Title
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    Now as u notice in ur text's form the denomin is WITHOUT the square

    • 2 years ago
  114. AravindG Group Title
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    yep how?

    • 2 years ago
  115. Mikael Group Title
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    They "transfered" one "sqrt of the denominator" as original y TO THE DENUMERATOR

    • 2 years ago
  116. Mikael Group Title
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    In fact\[\frac{ 1*(x-2)(x-3) - (x-7)*(Monomial ) }{(x-2)^2(x-3)^2} =\]

    • 2 years ago
  117. AravindG Group Title
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    i see

    • 2 years ago
  118. AravindG Group Title
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    then how did 2x-5 come?

    • 2 years ago
  119. AravindG Group Title
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    wait i gt it !! 2x-5 is differential of x^2-5x+6 !!

    • 2 years ago
  120. Mikael Group Title
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    \[=\frac{ 1 - (x-7)*(Monomial) *((x-2)(x-3))^{-1}}{ (x-2)(x-3)} \]

    • 2 years ago
  121. Rohangrr Group Title
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    @AravindG Interact with this one : http://demonstrations.wolfram.com/TangentToACurve/

    • 2 years ago
  122. Mikael Group Title
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    \[= \frac{ 1 - Monomial*{Original Function} }{ (x-2)(x-3)} =\]

    • 2 years ago
  123. Mikael Group Title
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    \[= \frac{ 1 - y*Monomial }{ (x-2)(x-3) }\]

    • 2 years ago
  124. AravindG Group Title
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    gt it !!! thx a lot!!!

    • 2 years ago
  125. Mikael Group Title
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    I have given you a complete calculation

    • 2 years ago
  126. Mikael Group Title
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    And thx is due

    • 2 years ago
  127. Mikael Group Title
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    Close this question afterwards

    • 2 years ago
  128. AravindG Group Title
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    i knw d rest

    • 2 years ago
  129. AravindG Group Title
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    my only doubt is why i didnt get it by logarithmic differentiation

    • 2 years ago
  130. Mikael Group Title
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    What does it mean ?

    • 2 years ago
  131. AravindG Group Title
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    show u sas new qn

    • 2 years ago
  132. AravindG Group Title
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    closing thisone as page lagging

    • 2 years ago
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