Esercizi svolti di analisi reale e complessa - Dipartimento di ...

f(x, y) = (x + 3y)e −xy
f(x, y) = x 2 y
D ≡ {x 2 + y 2 ≤ 1}
∂
∂xi g(|x|) x ∈ Rn \ {0} g
C 1 ((0, +∞))
log (s + t)
(s0, t0) = (1, 0)
log (x − y 2 )
(x0, y0) = (1, 0)
f(x, y) ≡
ye
0 x = 1
y
−( x−1 )2 x = 1
f ∈ C∞ (R2 \ {(1, 0)})
f (1, 0)
f
δ > 0 |f(x, y) − f(x0, y0)| < 1
100 |(x, y) − (x0, y0)| < δ
(x0, y0) = (1, 1) f (1, 0) (x0, y0) = (1, 0)
∂f
∂x
f(x) = n
i=1 x2 i
f(x) = (x1 + x 2 2 , cos (x1x2)) x ∈ R n n ≥ 2
f(x, y, z) = y
z−x 2
∂f
∂x
N x0 = 0
|x| sin |x| (x ∈ R n )