Term
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Definition
| an ordered, unending list or numbers |
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Term
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Definition
We say that {an} converges to the real number L, or has the LIMIT L, and we write:
lim an = L
n->oo
provided that an can be made as close to L as we please merely by choosing n to be sufficiently large. That is, any number E > 0, there exists an integer N such that
|an-L| < E for all n >= N. |
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Term
| Substitution law for Sequences |
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Definition
If lim f(an) = A and the function f
n->oo
is continuous at x = A, then
lim f(an) = f(A)
n->oo |
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Term
| Squeeze Law for Sequences |
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Definition
If an <= bn <= cn for all n and
lim an = L = lim cn
n->oo n->oo
then lim bn = L as well.
n->oo |
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Term
| Limits of Functions and Sequences |
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Definition
If an = f(n) for each positive integer n, then
lim f(x) = L implies that lim an = L
n->oo n->oo |
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