Graphics Reference
In-Depth Information
By considering the two null sequences (1/2
n
) and (1/(2
n
)
provethat thefunction
f
is not continuous at
x
0 whatever value
k
may have.
)
21 (
Weierstrass
, 1874) Define the function
f
:
R
R
by
f
(
x
)
x
sin(1/
x
) when
x
0,
f
(0)
0.
Using thefact that
x
f
(
x
)
x
for all
x
, and qn 6.36, prove
that
f
is continuous at
x
0.
Prove from the definition of derivative that
f
is not differentiable at
x
0.
22 Define the function
f
: R
R by
f
(
x
)
x
sin(1/
x
) when
x
0,
f
(0)
0.
By methods similar to those of qn 21, prove that
f
is continuous at
x
0.
Provealso that
f
is differentiable at
x
0.
