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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
x
sin
1
x
,
x
≠
0
0
,
x
=
0
f(x) = \begin{cases} x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}
f
(
x
)
=
{
x
sin
x
1
,
0
,
x
=
0
x
=
0
and
g
(
x
)
=
{
x
2
sin
1
x
,
x
≠
0
0
,
x
=
0
g(x) = \begin{cases} x^2 \sin \frac{1}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}
g
(
x
)
=
{
x
2
sin
x
1
,
0
,
x
=
0
x
=
0
Discuss the graph for
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
, and evaluate the continuity and differentiability of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
.
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