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1) Find
a)
b)
c)
d)
e)
2) If
which of the following is true about
y = f ( x)?
a)
f
has a local minimum at
x = 5 and a point of inflection at
x = 10.
b)
f
has a local minimum at
x = 5 and a local maximum at
x
= 10.
c)
f
has a point of inflection at
x = 5 and a local minimum at
x = 10.
d)
f
has a point of inflection at
x = 5 and a local maximum at
x = 10.
e)
f
has a local maximum at
x = 5 and a local minimum at
x
= 10.
A curve is described by parametric equations where t > 0. Give an expression for
a)
b)
c)
d)
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e)
4) Give the value for
a)
b)
c)
d)
e)
Which of the following series converge?
I.
II.
III.
I and II only
II only
II and III only
I only
I, II and III
6) If
g
(
f
(
x
)) =
x
g
g
f
'(2) is
, (4) = 2 and
'(4) = 11, then
a)
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b)
c)
d)
e)
7) If f is a differentiable function and f (0) = -2 and f (5) = 4, then which
of the following must be true?
I. There exists a c in [0,5] where f ( c) = 0.
II. There exists a c in [0,5] where f ' ( c) = 0.
III. There exists a c in [0,5] where f ' ( c) = 6/5.
a) II only
b) I only
c) I and III only
d) II and III only
e) I, II and III
8) Evaluate
a)
b)
c)
d)
e)
9) Find the area enclosed by the graphs