Let K1 ⊃ K2 ⊃ K3 ⊃ ... be a sequence of bounded closed sets. Let...
Let K1 ⊃ K2 ⊃ K3 ⊃ ... be a sequence of bounded closed sets. Let (an) be a sequence of numbers with the property an ∈ Kn \ Kn+1. Show that (an) has a subsequence that converges to a point a ∈ ??∩Kn. Carefully state which theorems you are using.
Homework Answers
k0 = 3, k1 = 3^3 , k2 = 3^3^3 , k3 = 3^3^3^3 , ....
k0 = 3, k1 = 3^3 , k2 = 3^3^3 , k3 = 3^3^3^3 , . . . where k0 = 3 and kn+1 = 3^kn for n ≥ 0. What are the last two digits in k3 = 3^3^3^3 ? Can you say what the last three digits are? Show that the last 10 digits of ky are the same for all y ≥ 10.
2. Let {xn}nEN be a sequence in R converging to x 0. Show that the sequence R. Assume that x 0 an...
2. Let {xn}nEN be a sequence in R converging to x 0. Show that the sequence R. Assume that x 0 and for each n є N, xn converges to 1. 3. Let A C R". Say that x E Rn is a limit point of A if every open ball around x contains a point y x such that y E A. Let K c Rn be a set such that every infinite subset of K has a limit...
Corollry 12(Sequential ceriterion of a closed set) Let (M. Corollary 12 (Sequential criterion of ...
lemma 13
Corollry 12(Sequential ceriterion of a closed set) Let (M. Corollary 12 (Sequential criterion of a closed set) Let (M,d) be a met- ric space. A set S C M is closed if and only if for every sequence (xn) in S that converges in M, the limit of the sequence also belongs to S. Lemma 13 Let (an) be a sequence in (M, d). Let a M. Then, a is a limit point of (ra) if and only...
K0 = 3, k1 = 3^3 , k2 = 3^3^3 , k3 = 3^3^3^3 , . . . where k0 = 3 and kn+1 = 3^kn for n ≥ 0. What...
k0 = 3, k1 = 3^3 , k2 = 3^3^3 , k3 = 3^3^3^3 , . . . where k0 = 3 and kn+1 = 3^kn for n ≥ 0. What are the last two digits in k3 = 3^3^3^3 ? Can you say what the last three digits are? Show that the last 10 digits of ky are the same for all y ≥ 10.
5. Let (In be a nested sequence of closed bounded intervals. For each n E N,...
5. Let (In be a nested sequence of closed bounded intervals. For each n E N, let Xn E In. Use the Bolzano-Weierstrass Theorem to give a proof of the Nested Intervals Property
Consider the closed loop system a) Design a PD controller (that is, calculate K1 and K2) such that the system is stable and the steady-state error for the input r (t) = unity ramp let less than or equal to 0.02. b) Select a value from K1 and K2 and build
Consider the closed loop systema) Design a PD controller (that is, calculate K1 and K2) such that the system isstable and the steady-state error for the input r (t) = unity ramp letless than or equal to 0.02.b) Select a value from K1 and K2 and build the model in Simulink or solutionanalytical to obtain the response of the system to the magnitude rampr (t) = 2t.c) Graph the answer
***You must follow the comments*** Topic: Mathematical Real Analysis - Let (xn) be a bounded sequence...
***You must
follow the comments***
Topic: Mathematical
Real Analysis
- Let (xn) be a
bounded sequence ((xn) is not necessarily convergent), and assume
that yn → 0. Show that lim n→∞ (xnyn) = 0.
Question1.
All the
solution state that there exists M >0 and xn<=M . My question
is that why M always be bigger than 0 and Why it is bounded above ?
why it is not m<=xn bounded below????
Question.
2.
if the
sequence is convergent, then...
(5) Let {fn} be a sequence in C((0, 1]) which converges uniformly (to C([0, 1]). Prove that {fn} is uniformly bounded a...
(5) Let {fn} be a sequence in C((0, 1]) which converges uniformly (to C([0, 1]). Prove that {fn} is uniformly bounded and equicontinuous function f E a
(5) Let {fn} be a sequence in C((0, 1]) which converges uniformly (to C([0, 1]). Prove that {fn} is uniformly bounded and equicontinuous function f E a
Given condition: k1=k2=k3=k4=k5=k,F3=P, and nodes 1,2,5 are fixed Decision a.Global stiffness matrix b. Displacement of nodes...
Given condition: k1=k2=k3=k4=k5=k,F3=P, and nodes 1,2,5 are fixed
Decision
a.Global stiffness matrix
b. Displacement of nodes 3 and 4
c. Reaction force at nodes 1,2,5
d.Internal force of spring 2,4,5
Oh, and I would appreciate it if you could tell the answer using
computer typing instead of handwriting.
Because I don't know the cursive
If it is difficult, I would appreciate it if you could respond
in a convenient way.
1.7 한 스프링계가 아래와 같다. k2 ki -F3 Amino k4...
Let (xn) be a bounded sequence of real numbers, and put u = lim supn→∞ xn . Let E be the set consisting of the limits of all convergent subsequences of (xn). Show that u ∈ E and that u = sup(E). Form...
Let (xn) be a bounded sequence
of real numbers, and put u = lim supn→∞ xn . Let E be the set
consisting of the limits of all convergent subsequences of (xn).
Show that u ∈ E and that u = sup(E).
Formulate and prove a similar result for lim infn→∞ xn .
Thank you!
7. Let (Fm) be a bounded sequence of real numbers, and put u-lim supn→oorn . Let E be the set consisting of the limits of...
2. Let {xn}nEN be a sequence in R converging to x 0. Show that the sequence R. Assume that x 0 and for each n є N, xn converges to 1. 3. Let A C R". Say that x E Rn is a limit point of A if every open ball around x contains a point y x such that y E A. Let K c Rn be a set such that every infinite subset of K has a limit...
lemma 13
Corollry 12(Sequential ceriterion of a closed set) Let (M. Corollary 12 (Sequential criterion of a closed set) Let (M,d) be a met- ric space. A set S C M is closed if and only if for every sequence (xn) in S that converges in M, the limit of the sequence also belongs to S. Lemma 13 Let (an) be a sequence in (M, d). Let a M. Then, a is a limit point of (ra) if and only...
5. Let (In be a nested sequence of closed bounded intervals. For each n E N, let Xn E In. Use the Bolzano-Weierstrass Theorem to give a proof of the Nested Intervals Property
***You must
follow the comments***
Topic: Mathematical
Real Analysis
- Let (xn) be a
bounded sequence ((xn) is not necessarily convergent), and assume
that yn → 0. Show that lim n→∞ (xnyn) = 0.
Question1.
All the
solution state that there exists M >0 and xn<=M . My question
is that why M always be bigger than 0 and Why it is bounded above ?
why it is not m<=xn bounded below????
Question.
2.
if the
sequence is convergent, then...
(5) Let {fn} be a sequence in C((0, 1]) which converges uniformly (to C([0, 1]). Prove that {fn} is uniformly bounded and equicontinuous function f E a
(5) Let {fn} be a sequence in C((0, 1]) which converges uniformly (to C([0, 1]). Prove that {fn} is uniformly bounded and equicontinuous function f E a
Given condition: k1=k2=k3=k4=k5=k,F3=P, and nodes 1,2,5 are fixed
Decision
a.Global stiffness matrix
b. Displacement of nodes 3 and 4
c. Reaction force at nodes 1,2,5
d.Internal force of spring 2,4,5
Oh, and I would appreciate it if you could tell the answer using
computer typing instead of handwriting.
Because I don't know the cursive
If it is difficult, I would appreciate it if you could respond
in a convenient way.
1.7 한 스프링계가 아래와 같다. k2 ki -F3 Amino k4...
Let (xn) be a bounded sequence
of real numbers, and put u = lim supn→∞ xn . Let E be the set
consisting of the limits of all convergent subsequences of (xn).
Show that u ∈ E and that u = sup(E).
Formulate and prove a similar result for lim infn→∞ xn .
Thank you!
7. Let (Fm) be a bounded sequence of real numbers, and put u-lim supn→oorn . Let E be the set consisting of the limits of...
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