Question

In: Advanced Math

Just (c) from the problem below: 1.11. Let f be a one-to-one smooth map of the...

Just (c) from the problem below:

1.11. Let f be a one-to-one smooth map of the real line to itself. One-to-one means that if f(xi) = f(x2), then x1 = x2. A function f is called increasing if x1 〈 x2 implies

f(x1 )くf(x2), and decreasing if x1 〈 x2 implies f(x1 ) 〉 f(x2 )

(a) Show that f is increasing for all x or f is decreasing for all:x

(b)Show that every orbit {x0, x1, x2…} of f2 satisfies either xo

x1x2… or xox1x2...

(c) Show that every orbit of f2 either diverges to +

or- or converges to a

fixed point of f2.

(d) What does this imply about convergence of the orbits of f?

Solutions

Expert Solution


Related Solutions

Let f: A→B and g:B→C be maps. (A) If f and g are both one-to-one functions,...
Let f: A→B and g:B→C be maps. (A) If f and g are both one-to-one functions, show that g∘f is one-to-one. (B) If g∘f is onto, show that g is onto. (C) If g∘f is one-to-one, show that f is one-to-one. (D) If g∘f is one-to-one and f is onto, show that g is one-to-one. (E) If g∘f is onto and g is one-to-one, show that f is onto. (Abstract Algebra)
Let a < c < b, and let f be defined on [a,b]. Show that f...
Let a < c < b, and let f be defined on [a,b]. Show that f ∈ R[a,b] if and only if f ∈ R[a, c] and f ∈ R[c, b]. Moreover, Integral a,b f = integral a,c f + integral c,b f .
Let A ⊆ R, let f : A → R be a function, and let c...
Let A ⊆ R, let f : A → R be a function, and let c be a limit point of A. Suppose that a student copied down the following definition of the limit of f at c: “we say that limx→c f(x) = L provided that, for all ε > 0, there exists a δ ≥ 0 such that if 0 < |x − c| < δ and x ∈ A, then |f(x) − L| < ε”. What was...
1. Let T : Mn×n(F) → Mn×n(F) be the transposition map, T(A) = At. Compute the...
1. Let T : Mn×n(F) → Mn×n(F) be the transposition map, T(A) = At. Compute the characteristic polynomial of T. You may wish to use the basis of Mn×n(F) consisting of the matrices eij + eji, eij −eji and eii. 2.  Let A = (a b c d) (2 by 2 matrix) and let T : M2×2(F) → M2×2(F) be defined asT (B) = AB. Represent T as a 4×4 matrix using the ordered basis {e11,e21,e12,e22}, and use this matrix to...
Let f be a one-to-one function from A into b with B countable. Prove that A...
Let f be a one-to-one function from A into b with B countable. Prove that A is countable. Section on Cardinality
Let f:A→B and g:B→C be maps. (a) If f and g are both one-to-one functions, show...
Let f:A→B and g:B→C be maps. (a) If f and g are both one-to-one functions, show that g ◦ f is one-to-one. (b) If g◦f is onto, show that g is onto. (c) If g ◦ f is one-to-one, show that f is one-to-one. (d) If g ◦ f is one-to-one and f is onto, show that g is one-to-one. (e) If g ◦ f is onto and g is one-to-one, show that f is onto.
Let l:ax1+bx2 =c be a line where a^2+b^2 =1.Find the map f: R^2 →R^2 that represents...
Let l:ax1+bx2 =c be a line where a^2+b^2 =1.Find the map f: R^2 →R^2 that represents the reflection about l. Verify that the transformation f found in Problem 1 is an isometry.
TOPOLOGY Let f : X → Y be a function. Prove that f is one-to-one and...
TOPOLOGY Let f : X → Y be a function. Prove that f is one-to-one and onto if and only if f[A^c] = (f[A])^c for every subset A of X. (prove both directions)
Let f: X→Y be a map with A1, A2⊂X and B1,B2⊂Y (A) Prove f(A1∪A2)=f(A1)∪f(A2). (B) Prove...
Let f: X→Y be a map with A1, A2⊂X and B1,B2⊂Y (A) Prove f(A1∪A2)=f(A1)∪f(A2). (B) Prove f(A1∩A2)⊂f(A1)∩f(A2). Give an example in which equality fails. (C) Prove f−1(B1∪B2)=f−1(B1)∪f−1(B2), where f−1(B)={x∈X: f(x)∈B}. (D) Prove f−1(B1∩B2)=f−1(B1)∩f−1(B2). (E) Prove f−1(Y∖B1)=X∖f−1(B1). (Abstract Algebra)
Need this in C#. Below is my code for Problem 3 of Assignment 2. Just have...
Need this in C#. Below is my code for Problem 3 of Assignment 2. Just have to add the below requirement of calculating the expected winning probability of VCU. Revisit the program you developed for Problem 3 of Assignment 2. Now your program must calculate the expected winning probability of VCU through simulation. Run the simulation 10,000 times (i.e., play the games 10,000 times) and count the number of wins by VCU. And then, calculate the winning probability by using...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT