Homework
1. Calculate the limit
sin(x3 + y 3 )
.
(x,y)→(0,0)
x2 + y 2
lim
2. Let
f (x, y) =
x sin
!
1
, y ̸= 0,
y
0,
y = 0.
Find all points (x, y) at which f (x, y) is continuous.
3. (1) Prove that
lim xx = 1.
x→0+
Hint: If a > 0, then a = eln a .
(2) Calculate the limit
lim
(x,y)→(0,0)
1
2 4
(x2 + y 2 )x y .
0
