#### Answer

a) $-x+2y+1$ b) $-e^3+2e^3y-2e^3$

#### Work Step by Step

a. As we know that $L(x,y)=f(x,y)+f_x(x-m)+f_y(y-n)$
Here, we have $f_x=-1$; and $f_y=2$
Thus, we get $L(0,0)=1+(-1)(x-0)+2(y-0) \\ \implies L(0,0)=-x+2y+1$
b. As we know that $L(x,y)=f(x,y)+f_x(x-m)+f_y(y-n)$
Here, we have
$f_x=-e^3$; and $f_y=2e^3$
Thus, we get $L(1,2)=e^3-e^3(x-1)+2e^3(y-2)
\\ \implies L(1,2)=-e^3+2e^3y-2e^3$