* Ex. 4. Examine existence of the double

Question

* Ex. 4. Examine existence of the double integral and iterated integrals
of the given function over the given set R, and prove your conclusion.
(6) g(x,y)
- Leshrane
sin(1) sin(1) if xy +0,
if xy = 0,
R=
= (0,1) > (0, 1).
x
=

Kunduz · Accepted Answer

2
polynomial so it is
.
Right Hand limit :-
tim f(x) = lim (x²) sin I
- of
atot
flas: . (
--
solution: When xto, ² is a
continuous sin()
aho continuous as ato.
Hence, f(x) continuous for ato.
When xoo,
teft hand limiti
lim Fle)
f(x) = line (-x²) sin I
no
As x is
As n is
close to o
very
but noto sinta
:. sin .
k (a constant)
2
(ar constant)
- lim K(-x2)
k
= lim al02) = 0
atot
K(0) 20
And flo) = otsin (176)
otsin (1) = 0
;
teace, left hand
fro)
limit
limit
= f(x) is continuous at a=0
very close to o but
noto
3
-
2101
2
.
O
Right Hand
also

* Ex. 4. Examine existence of the double integral and iterated integrals of the given function over the given set R, and prove y