17. Find the sum of the series
∞
summationdisplay
n
=1
n
2
n

1
.
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
(f) The series diverges.
18. Consider the polynomial 1

x
2
2!
as an approximation to cos(
x
) on the closed interval

1
≤
x
≤
1. What is the best bound on the error that is given by Taylor’s inequality?
19. What is the general solution of the differential equation
dy
dx
=

xy
y
2
+ 1
? What is the
behavior of the solutions as
x
→ ∞
?
20.
Which of the following curves is an orthogonal trajectory to the family of curves
x
2
4
+
y
2
9
=
C
, where
C
is an arbitrary positive constant?
3
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 Fall '08
 Temkin
 Math, Calculus

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