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gradient of lines parallel to the y-axis

Discussion in 'Mathematics' started by fudgesweets, Jan 13, 2012.

  1. fudgesweets

    fudgesweets New commenter

    If you differentiate x=1 for example, what is the answer?
     
  2. fudgesweets

    fudgesweets New commenter

    If you differentiate x=1 for example, what is the answer?
     
  3. PaulDG

    PaulDG Occasional commenter

    Differentiate with respect to what?
     
  4. It has a gradient of inifinity (which doesn't exist) of course!

    cyolba, opening a whole can of worms :)
     
  5. x=1
    Diff x wrt y gives
    dx/dy=0
    and use chain rule
    dy/dx=1/(dx/dy)
    gives dy/dx=1/0
    which gives the required result.
     
  6. Maths_Mike

    Maths_Mike New commenter

    The x axis has gradient 0. The y axis has gradient 1/0 (as above.)
    The product of the gradients of 2 perpendicular lines is -1

    1\0 x 0 = -1 [​IMG]
     
  7. Michael - that is naughty - behave! [​IMG]
     
  8. Maths_Mike

    Maths_Mike New commenter

    Sry - bit of a sense of humour failure!
     
  9. Yes, both 0/0 and 0 to the power 0 are classed as indeterminate values since they can be shown to take any value. For example limit as x tends to 3 of (x squared -9)/(x-3) tends to 0/0 but also tends to the value of 6. Using similar arguments you can shown that 0/0 tends to any value you choose.
     

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