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Limits & Continuity
Build intuition for approaching values and continuity.
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To show
f
(
x
)
=
x
3
−
x
−
1
f(x) = x^{3} - x - 1
f
(
x
)
=
x
3
−
x
−
1
has a root in
[
1
,
2
]
[1,2]
[
1
,
2
]
by the Intermediate Value Theorem, one checks the signs at the endpoints. Compute
f
(
2
)
f(2)
f
(
2
)
.
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x
f
( )
x
n
√
⌫
AC
7
8
9
+
4
5
6
−
1
2
3
×
0
.
a
b
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