pdf (it, 2.898,97 KB, 25/01/13)

2π
xt sin t
F (x) = e dt x ∈ R
0 t
x log(1 + xt)
G(x) =
0 1 + t2 dt x ∈ R
F (x, y) =
x
y
e −(x−t)2
dt
F (x) =
2π
e
0
x sin y dy
x = 0
y
F (y) =
0
log(1 + xy)
1 + x2 dx
F (x) =
y
x
0
e −xt2
dt − x
x = 0
x > 0
F (x) =
π
x
0
sin(xy)
y
f : R 2 → R
dy
f(x, y) = arcsin(xy).
f f
(x 2 + y 2 + 12ax + 9a 2 ) 2 = 4a(2x + 3a) 3 a > 0
y 4 − x 4 + ay 2 + bx 2 = 0 a, b ∈ R
f(x, y) = log arctan e (x2 +y4 ) 3
+ 1
(0, 0)
f(x, y) = 1/x + 1/y Ea =
{(x, y) ∈ R 2 : 1/x 2 + 1/y 2 = 1/a 2 , x = 0, y = 0} a > 0