MATH 205–08
Exam #2
Name:
For full credit show all of your work (legibly!), unless otherwise speciﬁed. Answers may include
all arithmetic operations, trigonometric functions, inverse trigonometric functions, and natural log
arithms. Algebraic simpliﬁcation of answers is unnecessary.
The problems are in no particular order, and it is suggested that you look at all of them before
beginning to answer any.
1.
(8 points)
The
cissoid of Diocles
is a curve satisfying the equation
x
(
x
2
+
y
2
) = 4
y
2
.
(a)
(6 points)
Find a formula for
dy
dx
on this curve.
(b)
(2 points)
Find the equation of the tangent line to the curve at (2
,

2).
2.
(6 points)
Calculate
d
dx
cos(
x
2
e
x
).
1
2
3
4
5
6
7
(8)
Σ
Page 1 of 4
1933 Kartika 6
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Exam #2
3.
(8 points)
Amy is standing motionless 50 meters east of a northsouth road with a radar
gun, while Bob, who is 120 meters to the north, is driving south. The radar gun reports
how quickly the
distance between Amy and Bob
is changing (which may not be Bob’s actual
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 Fall '08
 WILDSTROM
 Calculus, Algebra, Trigonometry, Inverse function, Logarithm, Inverse trigonometric functions

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