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10 Cards in this Set
- Front
- Back
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Sandwich Lemma |
Let (an) and (cn) be sequences with limit a. Let bn be a sequence such that there exists M where anM. Then bn has limit a. |
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Function has limit L at a |
For every e>0, theres a d>0 st if t-a |
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Uniform Convergence |
For e>0, we have n s.t fn(t)-f(t) < e for ann n>N and t in [a,b] |
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Completeness Property |
If U is bounded above then theres an upper bound s s.t if theres another upper bound s' for U then s |
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IVT |
f continuous on [a,b]. Suppose a |
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MVT |
Let f continuous on [a,b] and differentiable on (a,b). Then for c in (a,b) there is f'(c)=f(b)-f(a) / b-a |
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Min-max theorem |
f continous on [a,b] Theres x in [a,b] s.t f(t)f(x) |
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Hadamards Lemma |
f:I->R, a in I. f differentiable at a iff theres w:I->R s.t f(t) = f(a) + w(t-a) |
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Rolles Theorem (Like the MVT) |
Let f be continuous on [a,b] and differentiable on (a,b). Suppose f(a)=f(b)=0. Then theres c in (a,b) s.t f'(c)=0 |
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Uniformly Continuous |
If for e>0 theres d>0 s.t if x-y |
