Answer to Question #195209 in Calculus for Sourav

Question

Find the third Taylor polynomial of the function f(x,y)= =1+5xy+3²y at (1,2)

Answer 1

Given $f(x,y)=1-5xy+3^2y=1-5xy+9y$

$f(1,2)=1-5(1)(2)+9(2)=1-10+18=9$

$f_x=-5y\\ f_x(1,2)=-10 \\ f_y=-5x+9 \\ f_y(1,2)=-5(1)+9=4 \\ f_{xx}=0\\ f_{yy}=0 \\$

$f(x,y)=f(a,b)+(x-1)f_x(1,2)+(y-2)f_y+\dfrac{f_{xx}\times (x-1)^2}{2!}+....$

$=9+(x-1)\times -10+(y-2)\times 4+0+...\\[9pt]=9-10x+10+4y-8\\[9pt]=4y-10x+11$