Math22lO Quiz 7 (Sections 12.6-12.7)
Summer, 2012
V
Name
Dylan Zwick
Of
Date
Instructions: Please show all of your work as partial credit will be given where
appropriate, and there may be no credit given for problems where there is no work
shown. All answers should be completely simplified, unless otherwise stated.
1. (15 points) Find
y—s—t
,
and
2
z=t
using the chain rule for
.
w_eXZ given
Express your answer in terms of s and t.
()
/
\7
•1
v
ye
7
y
9
I
.
XY
V
(
(7+Yt
Answer:
x=s+t
using the chain rule for
2. (10 points) Find
t
2
y—sec
1n-- given
x=tant
,
and
Express your answer in terms oft.
±
-
fr
±
c
-
Z
4
-
V
/
ec4f
y
ec
—
L
Answer:
3. (15 points) Find a point on the surface
is parallel to the plane 8x—3y—z=O
+3y where the tangent plane
2
z2x
6 Y/ -i)
l
yi
27h(-i)
/
Answer:
Z
‘
/
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