7/21/2019 Questo 1 Calculo 2

1/1

(7)(7

(1)(1)

(6)(6)

(2)(2)

(5)(5)

(4)(4)

(3)(3)

hd x,y /x

3$yKx$y

3

x2Cy

2; (software: maple 14)

x,y /x

3yKxy

3

x2Cy

2

plot3d h x,y ,x =K2 ..2,y =K2 ..2 ;

limit h x,y , y = 0,x = 0 ;

limit x

3yKxy

3

x2Cy

2, x = 0,y = 0

x3yKxy

3

x2Cy

2

x3yKxy3

x2Cy

2

differentiate w.r.t. y

x3K3 xy

2

x2Cy

2 K

2 x3yKxy

3y (d/dy)

x2Cy

2 2

differentiate w.r.t. x

3 x2K3 y

2

x2Cy

2 K

2 3 x2yKy

3y

x2Cy

2 2 K

2 x3K3 xy

2x

x2Cy

2 2 C

8 x3yKxy

3xy (d2/dydx)

x2Cy

2 3

differentiate w.r.t. x

3 x2yKy

3

x2Cy

2 K

2 x3yKxy

3x (d/dx)

x2Cy

2 2

differentiate w.r.t. y

3 x2K3 y

2

x2Cy

2 K

2 3 x2yKy

3y

x2Cy

2 2 K

2 x3K3 xy

2x

x2Cy

2 2 C

8 x3yKxy

3xy (d2/dxdy)

x2Cy

2 3