M408C
Practice problems for Exam #2
Directions
. Indicate the correct answer for each problem by filling in the appropriate space, as in (A) (
•
) (C) (D) (E).
1) If
f
(
x
) and
g
(
x
) are continuous for all
x
, which function below might
not
be continuous for all
x
?
(A)
f
(
g
(
x
)).
(B)
braceleftbigg
xf
(
x
)
,
x
≤
0
xg
(
x
)
,
x >
0
.
(C)
f
(
x
)
3

cos(
g
(
x
))
.
(D)
braceleftbigg
f
(
g
(
x
))
,
x
≤
0
g
(
f
(
x
))
,
x >
0
.
(E)

f
(
x
)
g
(
x
)

.
2) For
f
(
x
) as shown, on what subset of [

2
,
4] is
f
′
(
x
)
≤
0.
0
1
2
4
3
x
2
1
y
y = f(x)
(A) [

2
,

1]
∪
[1
,
3].
(B) [

1
,
1)
∪
[3
,
4].
(C) [

2
,
1].
(D) [1
,
3].
(E) [

1
,
1]
∪
[3
,
4].
3) The position
s
[cm] of a particle at time
t
[sec] is given by
s
(
t
) = 3 tan(2
t
),
t
≥
0. What is the acceleration of the particle
at time
t
=
π/
8?
(A) 36cm
/
sec
2
.
(B)

12cm
/
sec
2
.
(C) 32cm
/
sec
2
.
(D) 48cm
/
sec
2
.
(E)

24cm
/
sec
2
.
4) If
f
(
x
) is continuous for all
x
and satisfies
f
(0) =

2 and
f
(1) = 3, which statement below could be
false
?
x
→
c
f
(
x
) exists for all
c
.
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 Fall '07
 Ambler
 Celsius, Continuous function, The Tangent

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