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Problem #3
.
Consider the two surfaces in space:
S
1
:
x
2
+
y
2
=
a
2
and
S
2
:
z
=
b
2
xy
.
These surfaces intersect
on a curve in space, ±
nd a parametric representation for this curve.
C
REDIT
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Problem #2
.
Consider the two curves in
R
3
which are parameterized as follows:
C
URVE
1:
(
t
)
=
(
t
, 1–
t
, 3+
t
2
)
C
URVE
2:
(
s
)
=
(3–
s
,
s
–2,
s
2
)
with 0 ≤
s
,
t
<
∞.
Show that (by a miracle) these curves intersect – and ±
nd the point of intersection.
C
REDIT
2
1
0
Problem #1
.
A particle spirals out from the origin according to
x
(
t
) =
t
cos
t
, y(t) =
t
sin
t
; 0 ≤
t
<
∞.
Find
expressions for the distance from the origin (which is
not
the arclength) and the speed as a function of
t
.
Math 32A
Lecture #5
Fall 2007
Problem Set #4
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Problem Set #4
C
REDIT
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Problem #4
.
Consider the usual hyperbolic trig functions:
cosh
x
1
2
(e
x
±
e
²
x
)
sinh
x
1
2
(e
x
±
e
±
x
)
.
Derive the analog of the double angle formulas for these cases; that is to say expressions for cosh 2
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 Fall '08
 GANGliu
 Math

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