Graphics Reference
In-Depth Information
then
lim
f
(
x
)
l
,
lim
f
(
x
)
g
(
x
)
l
m
,
lim
f
(
x
) ·
g
(
x
)
l
·
m
and, provided
l
0, lim
1/
f
(
x
)
1/
l
.
94
Provethat lim
c
c
and lim
x
a
,
and use these results to develop theorems about limits of
polynomials and rational functions.
95 A function
f
: R
R is defined by
f
(
x
)
x
, when
x
2,
f
(2)
k
,
3
x
18
x
28, when
x
f
(
x
)
2.
Is there a value of
k
which will make
f
continuous at every point?
96 A real function
f
is continuous on [
a
,
b
]. A real function
g
is
continuous on [
b
,
c
].
a
b
c
and
f
(
b
)
g
(
b
). A function
F
is
constructed by
f
(
x
),
g
(
x
),
a
x
b
b
x
c
.
F
(
x
)
Provethat
F
is continuous on [
a
,
c
].
Thus if two continuous functions are'contiguous' (coincideat an
end point of their respective domains), thefunction formed by
joining them is continuous.
97 A function
f
: R
R is defined by
x
a
x
a
, for
x
a
, where
n
is a positive integer;
f
(
x
)
f
(
a
)
k
.
Is there a value of
k
which would makethefunction
f
continuous
at every point?
