Novo Documento 2018-01-20lymber/teaching/2017/mat2454-2017/prova… · Scanned by CamScanner lı...
Transcript of Novo Documento 2018-01-20lymber/teaching/2017/mat2454-2017/prova… · Scanned by CamScanner lı...
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W ı= ı= ııl ļ
Q u e s tã o 1 (V a ıo r 3 0 p o n to s) S eia f H 2> R d a d a p o r
" ", c a s o e x is m ĝį (o ,
o) · $(o , o)
b A fu n çã o f é d ife m n c iá v e l e m (0 , 0)?
. D e te m in e ,_ e x is ta ,
. D e riv a d a d ir e c io n a l ŜŚ(o , o), p a r a i = (39 , )
区九ば岫ļ cĹo 且
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lı■目 四四国 四国皿厦
g r ffic o n o p o n to (1, 2 g j1 ,
2 )) d e s c r ito p e la e q u a çã o
Q u e s tã o 2 (V a ıo r 2 0 p o n to s) S e ja g : 2 Þ R u m a ħm çä o d e c la s s e C -c o m p】a n o ta n g m te a o
4 x 4 5y + 4 z + 6 0 0
a D e be rm in e g j1, 2) e V g jl 2)
b S e h R 3 m é d a d a p o r h (x , y , z ) = z g (x y , y), d e te rm in e o p ]a n o ta n g e n te à s u p e r H c ie
n o p o n to (3 , 2 2)
Q m Z
Q ) (1 , 2
, 3 CI, 2 )) e c n o ?ıc m o Ųx Ąs y .
Lł 2 + 6
ų 9 0 + L ļ 3 (ıı 2 ) + Ġ O = 0
h Ĺ , Y \ ı) = Z
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r르으 (飞 り,尹。 よ ー 红リ, リ,
? TĻ
回
9 C ı I Z ) = l
@ a Q u a Ý , o d ? pla n Đ v k n w �
Lo 吕臼,
= ユ \)( \ 寺 箐( \. .
8 2
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Q v o ] 3 A leiĄeÝ 0 d o p l Q Q o Q � i? pw , jn @ ? Ļ
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(M O u u c ļ D 0 ţ l o d n
m 0 ħķ l
+ > x = o m x = e 2 3
X ◆ Y - 0 4 2 = Į C A A) Į h'
P A T O to , O , į )
久◆ 气- Į e = 4 13 C A ÑL O N TO P t
, V 3 ,
\ l3 )
S IE Ż U X L4 c 0
Ż - X + b ı = ) Į .
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Q = 1 X t j
dĮĐ s ru À u U d& LQfìa \ )
C A ◆ J A T O S
Ląa , 2 t
,ı/ =
" 9
(j , O , o ) = o
w m d e e m c ę (o 1 J ıo )
s ćio y n iyıiitvto ļ d e ę m c B
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1 I I ı ı = j + 1 /6 /5 5 +
Q u e s tão 4 (V a lo r 3 0 p o n to s) S eja f R 2> R d a d a p o r f(x , y ) = x
2y x y + 4y
3
a D e te rın in e o s p o n to s c d tic o s d e f e classffiquos
b D e te rm in e , s e h o u v e r, o s p o n to s d e m áx im o e m in im o d e f re s tr ita a o c o n ju n to
T = {(x , y) � 双2 0 ś y ś x e o ś × ś 1}
Q Lí
se ' " tz, f ' · y = o Ć b - '
(ı, ) = b
P d e sela
e' T d ņ ae laĤ G , o ) · dŁQt Io ļ l = ĺ (l,O )
ïı o l
H (l/z ,
'ł刚 - ' " J俨 如I·。
CVz , l e
'
w ]n d 9
(V2,
æ ) e'
P c R9
( , %6 ) >o �
m u'
n im o ıo c a Q
o xz
Ļ U Q� t
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Q u e s tão 4 (V a lo r 3 0 p o n to s) S eja f R 2 4 R d a d a p o r f(x , y) = x
2y x y + 4 y
3
a D e te M e o s p o n to s c rftic o s d e f e c la s s iliq u e o s
b d e te rm in e i s ė h o u v e r o s p o n to s d e m a x im o e w w w o d e f r e s tr ita a o c o n jtın to
T { (x , y) � R2
: 0 ś y ś x e O ś × ś 1}
(o ıo t
Y - .
U P ) q Cx ,
C ) - o, V x e to ,
Ł 3
O ļ b ļ L
? ıo )
2 ) Ļ Q J 0 Ţ d m o
Lţ C L © d jw im T m lo
u m o : Ţ%"
4 m T -' ( '
, o = ?
tp o A y ? " " · ë n T , / z ,
) ı, q R
Q f a o 4 Ļ
ı y \ p e T w a D J D Į