Examples:
1. lim (5x − 3) = 12.
x→3
2x2 + 4x − 16
2. lim
= 12.
x→2
x−2
3. lim (x2 − 3x + 1) = 11.
x→5
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THEOREM 20.2:
R
and let
c
Let f : D →
be an accumulation
point of D. Then
lim f (x) = L
x→c
if and only if for every sequence (sn)
in D such that sn → c, sn 6= c for
all n, f (sn) → L.
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THEOREM 20.3:
R
and let
c
Let f : D →
be an accumulation
point of D. The following are equivalent:
1. x→c
lim f (x)
does not exist.
2. There exists a sequence (sn) in
D such that sn → c, but (f (sn))
does not converge.
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