HW 206 Answers
3 a.
continuous?
i)
(0)
0
f
ii)
2
0
0
lim
( )
lim
0
x
x
f x
x
0
0
lim
( )
lim
0
x
x
f x
x
0
lim
( )
0
x
f x
iii) Since
0
(0)
lim
( ),
x
f
f x
( )
f
x
is continuous at
x=0.
differentiable?
0
0
lim
( )
lim 2
0
x
x
f
x
x
0
0
lim
'( )
lim1
1
x
x
f
x
Since
0
0
lim
( )
lim
( ),
x
x
f
x
f
x
( )
f
x
is not
differentiable at x = 0.
b.
not continuous and not differentiable at x = 1.