HW01 – gilbert – (55035)
1
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22
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JEG
C
001
10.0 points
Determine
x
lim
0
ë
x
1
x
2
−
x
1o
.
→
−
1. limit
=
1 correct
2. limit
=
−
1
2
3. limit
=
−
1
3
4. limit
=
1
3
5. limit
=
1
2
6. limit
=
−1
Explanation:
After simplification we see that
1
1
=
1 − (1 − x)
=
1
x − x
2
−
x
x(1 − x)
1 − x
for all x 6= 0.
Thus
limit
=
lim
1
=
1 .
−
002
10.0 points
Consider the slope of the given curve
at the five points shown.
List the five slopes in decreasing order.
1. A,
D,
B,
C,
E
2. E,
A,
C,
D,
B correct
3. B,
E,
D,
A,
C
4. B,
D,
C,
A,
E
5. A,
E,
D,
C,
B
6. E,
A,
B,
D,
C
Explanation:
The order will be the one from most
positive
slope
to
most
negative
slope.
Inspection of the graph shows that this is
E,
A,
C,
D,
B
.
003
10.0 points
The derivative, f
′
, of f
has graph
a
b
c
graph of f
′