# Exercici 11.10

kill(all)$

## Apartat a)

f(x,y):= x^3+y^2+x*y^2;

T[2](x,y) = taylor(f(x,y), [x,y], [1,2] , [2,2]);

ratsimp(%);

expand(%);

## Apartat b)

kill(all)$

f(x,y):=sin(x^2+y^2);

T[2](x,y) = taylor(f(x,y), [x,y], [0,0] , [2,2]);

ratsimp(%);

## Apartat c)

kill(all)$

f(x,y,z):= exp(x+y+z);

T[2](x,y) = taylor(f(x,y,z), [x,y,z], [0,0,0] , [2,2,2]);

ratsimp(%);

expand(%);