Question

The steady state temperature of certain medium is given by theta = e power 2x - 3 y. Find the linear approxmiation at (0,0)

Answer 1

$$\theta=e^{2x-3y}=e^{2x}*e^{-3y}=(1+(2x)+O(x^2))*(1-3y+O(y^2))=\\ =1+2x-3y+O(x^2)+O(x*y)+O(y^2)$$

linear approximation at (0,0) is equal to 1+2x-3y