Skip to main content
Menu
Lessons
Problems
Calculator
Search
Blog
Purchase
Login
Problems
Primary tabs
View
Problems
(active tab)
Show that all
x
satisfying
0
<
|
x
−
a
|
<
δ
is equivalent to the union
(
a
−
δ
,
a
)
∪
(
a
,
a
+
δ
)
where
a
is any real number and
δ
>
0
.
Prove that for any real numbers
a
and
δ
>
0
that the interval
(
a
−
δ
,
a
+
δ
)
contains the closed interval
[
a
−
δ
/
2
,
a
+
δ
/
2
]
.
GAIN AN ADVANTAGE
Fully worked out solutions
Easy to digest lessons
Cheat sheets
PDF: How to Make an A+ in Your First Calculus Course
CLICK HERE FOR INSTANT ACCESS
Lesson Specific Problems
Show that all
x
satisfying
0
<
|
x
−
a
|
<
δ
is equivalent to the union
(
a
−
δ
,
a
)
∪
(
a
,
a
+
δ
)
where
a
is any real number and
δ
>
0
.
Prove that for any real numbers
a
and
δ
>
0
that the interval
(
a
−
δ
,
a
+
δ
)
contains the closed interval
[
a
−
δ
/
2
,
a
+
δ
/
2
]
.
