wei (jw35975) – HW5 – milburn – (54685)
3
On the other hand,
lim
h
→
0
(
h
+ 7) = 7
,
by Properties of Limits. Consequently, the
given limit exists, and
limit = 7
.
keywords: limit, deFnition of derivative
007
10.0 points
±unctions
f
and
g
are deFned on (
−
10
,
10)
by their respective graphs in
2
4
6
8
−
2
−
4
−
6
−
8
4
8
−
4
−
8
f
g
±ind all values of
x
where the product,
fg
, of
f
and
g
is continuous, expressing your
answer in interval notation.
1.
(
−
10
,
−
2)
u
(
−
2
,
10)
2.
(
−
10
,
10)
correct
3.
(
−
10
,
−
2)
u
(
−
2
,
4)
u
(4
,
10)
4.
(
−
10
,
−
2]
u
[4
,
10)
5.
(
−
10
,
4)
u
(4
,
10)
Explanation:
Since
f
and
g
are piecewise linear, they are
continuous
individually
on (
−
10
,
10) except
at their ‘jumps’;
i.e.
, at
x
= 4 in the case
of
f
and
x
= 4
,
−
2 in the case of
g
. But
the product of continuous functions is again
continuous, so
is certainly continuous on
(
−
10
,
−
2)
u
(
−
2
,
4)
u
(4
,
10)
.