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Practice Problems Final sol

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Final
-
Practice
(redx-
(x,ex)
1.
->
2.
=
E
=
E
<1, 4)
=
-
3.
Use
x
(i + 1) 4;
3
=
3
+" (4:,p23
(42,42)
f
4:
+
+
(2x,2y,2z)
0f
Equ
y2 z2
x
=
=
line
normal
of
at(40,
Y0,z0)
4
=
l(t) 4 tof(P).
+
=
(X0 (1+2t),
Yr(1+2A),
=
Convince
the
line
passes
through
rigin.
Infact,
by
this
yourself
z0l1+2+)!
in
⑰
Xo
cartesian
=
coordinates
equ
I E!
=
is
given
5.
Max
(DuT(2,11)
(xft),Y'(t))
6:
x (t)
=>
=
-10U
15 (2,111
+
=
=
XT(x,y)
Y'(t)
=
-
1
7.
x
x7y2
=
ntsis
=>
n
->
Ri
(y-1)
0
-
=2.
r
01 p
=
2 Sinc
.
=
fr
8.
I,
F-dr
2)(x
=
R:oc
0
Sine
rE
0
=
dA
I
=
6,
9-
XXF
(4xF).
F-dr
=
Ids
=
=(0,0,3x4)
+E
z
If
2
1
n
19
=
1 0911
aS
z
-
fy2
F+
=
dA
y2
2
↑
I
E
16 x 4
+
z2
YE dA
=
(OxF.nds
(3xY-
dA
=
-
"is
***.nds
())
=
of-
(oxAdr
-r
14.
tysaA=Y!'
())
dudr
16-
*=(0,4,z)
M
n
I
F.
x
R:0-
idS
Z
-
1
1
&
4 1.
dA
I
=
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