Iteration diagrams and convergence

... yet met: a diverging cobweb. See if you can spot the important difference once you can see the 4 diagrams ...

... yet met: a diverging cobweb. See if you can spot the important difference once you can see the 4 diagrams ...

MATH 409, Fall 2013 [3mm] Advanced Calculus I

... interval [a, b] is also uniformly continuous on [a, b]. Proof: Assume that a function f : [a, b] → R is not uniformly continuous on [a, b]. We have to show that f is not continuous on [a, b]. By assumption, there exists ε > 0 such that for any δ > 0 we can find two points x, y ∈ [a, b] satisfying |x ...

... interval [a, b] is also uniformly continuous on [a, b]. Proof: Assume that a function f : [a, b] → R is not uniformly continuous on [a, b]. We have to show that f is not continuous on [a, b]. By assumption, there exists ε > 0 such that for any δ > 0 we can find two points x, y ∈ [a, b] satisfying |x ...

Multidimensional Calculus. Lectures content. Week 10 22. Tests for

... on (−1, 1), but the convergence is not uniform. It will be uniform if we restrict our attention to [−%, %] for % ∈ (0, 1). P → Theorem. Let fk →f on M . (i) If all fk are continuous on M , then also f is continuous there. (ii) If all fk have a derivative on M , then also f has it there and f 0 = ...

... on (−1, 1), but the convergence is not uniform. It will be uniform if we restrict our attention to [−%, %] for % ∈ (0, 1). P → Theorem. Let fk →f on M . (i) If all fk are continuous on M , then also f is continuous there. (ii) If all fk have a derivative on M , then also f has it there and f 0 = ...

Presentation on Weierstrass M-Test

... Any sequence that satisfies the Cauchy Criterion is known as a Cauchy sequence. The above theorem also shows that every convergent sequence is Cauchy, and every Cauchy sequence is convergent. COROLLARY 1: If is a Cauchy sequence that converges to Z, and N is chosen such that every such that , then f ...

... Any sequence that satisfies the Cauchy Criterion is known as a Cauchy sequence. The above theorem also shows that every convergent sequence is Cauchy, and every Cauchy sequence is convergent. COROLLARY 1: If is a Cauchy sequence that converges to Z, and N is chosen such that every such that , then f ...

Lesson 9.4 - Coweta County Schools

... … and why It is important to develop a strategy for finding the interval of convergence of a power series and to obtain some tests that can be used to determine convergence of a series. ...

... … and why It is important to develop a strategy for finding the interval of convergence of a power series and to obtain some tests that can be used to determine convergence of a series. ...

FABER FUNCTIONS 1. Introduction 1 Despite the fact that “most

... Now that we can use the Weierstrass M-test, we will prove a result that gives us the continuity of the limit of the above sort of series: Theorem 2. If (fk )k∈N is a sequence of continuous functions on [a, b] that converge uniformly to some f in [a, b], then f is continuous in [a, b]. Proof. Let (fk ...

... Now that we can use the Weierstrass M-test, we will prove a result that gives us the continuity of the limit of the above sort of series: Theorem 2. If (fk )k∈N is a sequence of continuous functions on [a, b] that converge uniformly to some f in [a, b], then f is continuous in [a, b]. Proof. Let (fk ...

Convergence

... A sequence of random variables converges in distribution to the random variable iff the sequence of cumulative distribution functions converges to at every point of continuity of: ...

... A sequence of random variables converges in distribution to the random variable iff the sequence of cumulative distribution functions converges to at every point of continuity of: ...

fn (x) = f(x). n2x if 0 ≤ x if 1 n ≤ x 0 if 2 n ≤ x ≤1

... for n=1). The idea is simply to choose a x that when plugged into a member of the sequence of functions (with n bigger than or equal to N) gives you the peak of one of the triangles. Well we use the same trick we choose an x that gives us a peak when we plug it into fN. Well the peak of this functio ...

... for n=1). The idea is simply to choose a x that when plugged into a member of the sequence of functions (with n bigger than or equal to N) gives you the peak of one of the triangles. Well we use the same trick we choose an x that gives us a peak when we plug it into fN. Well the peak of this functio ...

Document

... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...

... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...

Slide 1

... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...

... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...

Section 11.2: Series

... Convergence of a Series If lim S n S for some finite number S, then the n ...

... Convergence of a Series If lim S n S for some finite number S, then the n ...