微積分学演習第３回 1

微積分学演習第３回

1

f(x, y)

(1) f (x, y) = 1

2 x

− xy + y

(2) f (x, y) = x

− x

y

+ y

(3) f (x, y) = x

+ y

− 3x − 12y + 2 (4) f (x, y) = xy − log(x

+ y

)

2

3

(1) f (x, y) = sin x cos y (2) f (x, y) = e

sin(x + y) (3) f (x, y) = 1

1 − x − y (4) f (x, y) =

√ 1 − xy 1 + x + y

3

(1) x

− 2xy + 5y

= 2

x

+ 6y

(2) x

− 4xy − 2y

= 10

x

+ y

4

(1) f(x, y) = xy, D = {(x, y) | x

+ y

= a

}, a > 0.

(2) f(x, y) = x

+ y

, D = {(x, y) | 2x

+ y

≤ 4}.

(3) f(x, y) = x

+ y

− xy − 3x, D = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}.

5

a