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Math Help - More local linearization

  1. #1
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    More local linearization

    An unevenly heated plate has temperature T(x,y) in degrees celcius at the point (x,y). If T(2,1)=135, and Tx(2,1)=16 and Ty(2,1)= -15, estimate the temperature at the point (2.04, 0.97).
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  2. #2
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    Quote Originally Posted by dexza666 View Post
    An unevenly heated plate has temperature T(x,y) in degrees celcius at the point (x,y). If T(2,1)=135, and Tx(2,1)=16 and Ty(2,1)= -15, estimate the temperature at the point (2.04, 0.97).
    Where exactly are you stuck?

    Just substitute into the usual formula. To wit:

    T(x + \delta x, y + \delta y) \approx T(x, y) + T_x (x, y) \, \delta x + T_y (x, y) \, \delta y.

    Note that x = 2, y = 1, \delta x = 0.04 and \delta y = -0.03.
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  3. #3
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    T(2.04,0.97) ≈ 135 + (2.04-2)*16 + (0.97-1)*-15 = 136.09

    is this the answer?
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  4. #4
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    Quote Originally Posted by dexza666 View Post
    T(2.04,0.97) ≈ 135 + (2.04-2)*16 + (0.97-1)*-15 = 136.09

    is this the answer?
    Yes.
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