# Math Help - More local linearization

1. ## 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).

2. Originally Posted by dexza666
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 $\delta y = -0.03$.

3. T(2.04,0.97) ≈ 135 + (2.04-2)*16 + (0.97-1)*-15 = 136.09

is this the answer?

4. Originally Posted by dexza666
T(2.04,0.97) ≈ 135 + (2.04-2)*16 + (0.97-1)*-15 = 136.09

is this the answer?
Yes.