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9 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Converges to the limit |
A real sequence (an) converges to the limit L if, for each E>0 there exists N in Z^+ such that for all n>=N, |an-L| |
Exits N |
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Limit L at infinity |
Let D subset of R be unbounded above and f:DtoR. Then f has a limit L at infinity if, for each E>0, there exists K in R such that, for all x in D with x>K, |f(x)-L| |
Function Restate q K in X>K
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Cluster point |
Let D be a subset of R. Then a in R is a cluster point of D if, for each E>0, there exists x in D with 0<|x-a| |
D subset R
a |
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Limit L of a |
Let D be a subset of R, f:D to R and a be a cluster point of D. Then f has a limit L at a if, for each E>0, there exists delta>0 such that, for all x in D with 0<|x-a| |
For all x in D |
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f continuous at a |
Let f: D to R and a in D. Then f is continuous at a if, for all sequences (xn) in D such that xn to a, f(xn) to f(a). |
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f is continuous |
f is continuous if it is continuous at a for all a in D |
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Cauchy (or has the Cauchy property) |
A real sequence (an) is Cauchy (or has the Cauchy property) if, for each E>0, there exists N in Z^+ such that, for all n,m>=N, |an-am| |
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f is differentiable at a |
Let f : D to R, where D is some subset of R and a in D be a cluster point of D. Then f is differentiable at a if the limit Lim(x to a)[(f(x)-f(a))/(x-a)] exists. |
Let ,where D subset R
a
Limit exists |
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Differentiable |
We say that f is differentiable if it is differentiable at a for all a in D |
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