Using precise definitions of limits, prove that lim x → 0 f ( x ) does not exist: f ( x ) = { 1 i f x i s r a t i o n a l 0 i f x i s i r r a t i o n a l (Hint: Think about how you can always choose a rational number 0 < r < d, but | f ( r ) − 0 | = 1 .)
Using precise definitions of limits, prove that lim x → 0 f ( x ) does not exist: f ( x ) = { 1 i f x i s r a t i o n a l 0 i f x i s i r r a t i o n a l (Hint: Think about how you can always choose a rational number 0 < r < d, but | f ( r ) − 0 | = 1 .)
Using precise definitions of limits, prove that
lim
x
→
0
f
(
x
)
does not exist:
f
(
x
)
=
{
1
i
f
x
i
s
r
a
t
i
o
n
a
l
0
i
f
x
i
s
i
r
r
a
t
i
o
n
a
l
(Hint: Think about how you can always choose a rational number 0 < r < d, but
|
f
(
r
)
−
0
|
=
1
.)
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