Question

Find the linearization of the function f(x,y) = ye^x + 2x^2 y at the point (0,2) and use the result to approximate f (0.1, 1.9) to three decimal places.

Answer 1

$L(x,y)=f(a,b)+\frac{\partial f(x,y)}{\partial x}|_{a,b}(x-a)+\frac{\partial f(x,y)}{\partial y}|_{a,b}(y-b)$

$f(0,2)=2$

$f_x=ye^x+4xy$

$f_x(0,2)=2$

$f_y=e^x+2x^2$

$f_y(0,2)=1$

$L(x,y)=2+2x+y-2=2x+y$

$f(0.1,1.9)=0.2+1.9=2.100$