## Transcribed Text

Suppose
that
such
that
non
-2ero
y=2t,
y=2-s, =4s+1.
What is a common normal vector for the parallel planes P1, P2 where E lies on P1
P2?
(0, (4,1).
(2,2,4).
(2,-1,4).
P(-1,-1,2)
Does
lim
x2y
Yes.
Suppose
I(s,t).
y(s,t)
az|
ds
ls=0,f=l
(0,1
(3.
9
24
-6
Let F(21,22,23,24) 3x3).
Find the equation = 100 at the point (1, 17,1,0)
3x1 3r3 Dech
3x1 +I2 3r3 ,He
3(11 1)+(2)+3(23-1)+42x4 = 100
For what values of c does f(z,y) cr² my have local maximum the point
HIS
R.
c) 0
The area the C whose equation in polar coordinates is given
byr= /20 cos(0)i
-1
21-
MIA 1
Evaluate the integral by of variables.
OR cos(16x² 25y²)dA
where Ri the region the ellipse 16x² 25y²
1
Set up the triple integral 0052 xyz dV where Tis the solid tetrahedron with vertices (0,0,0).
(0,0,1),(1,0,0) and(0,1,0)
gltate xyz dzdydx
6's so xyz dzdydx
so
Evaluate $5e25d dy,where C'isthecurve = 237 from (0,1) to (2,e*)
3(e+ 1).
s(e+ e).
3(e4 -1).
3(et -2).
and let Co and Cs be circles unit
Then whicho the following statements true?
Oand
F . dr € 0 and for
for dr 0and
field. Which following expressions meaningful?
grad(curl
curl(din Fi
Find the equation the tangent planet the given parametric surface at the specified point
x 2u²,y v2 uv; (2,1,1)
-2x +2y+32z=0
x 2y-32z
15x 2y+32x
-x 2y+4x=0
Let F(z. 2) be the gradient vector field of f(x let C be the curve the
intersection the plane y x² if 1.orlented ounterclockwise
evaluate dr.
None of the above.
Let Ebe: with boundary surface S with positive (outward) orientation The
volume of

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