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Limits & Continuity
Build intuition for approaching values and continuity.
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For
lim
x
→
2
(
3
x
+
1
)
=
7
\lim_{x\to 2}(3x + 1) = 7
lim
x
→
2
(
3
x
+
1
)
=
7
,
find the largest
δ
>
0
\delta > 0
δ
>
0
such that
∣
(
3
x
+
1
)
−
7
∣
<
0.03
|(3x+1) - 7| < 0.03
∣
(
3
x
+
1
)
−
7∣
<
0.03
whenever
0
<
∣
x
−
2
∣
<
δ
0 < |x - 2| < \delta
0
<
∣
x
−
2∣
<
δ
.
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( )
x
n
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AC
7
8
9
+
4
5
6
−
1
2
3
×
0
.
a
b
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