Problem 6. Let g.(r) c- for in an interval L. Find L and c so that logistic map Q4(z) = 42(1-1) i...
Problem 6. Let g.(r) c- for in an interval L. Find L and c so that logistic map Q4(z) = 42(1-1) is linearly conjugate with ge Vía a lone omorphism h : [0.1] → L. Find the linear function h
8. Problem 8. Let f and g map R into itself where /(x) and g(x) = Show that if f is conjugate to g via a homeomorphism h, then either h or h 1 is not differentiable.
1. Problem 1. p.105 N 1. Let fu (x) (2-- for in some interval L. Determine L so that ,, is conjugate with Qμ We were unable to transcribe this image
1. Problem 1. p.105 N 1. Let fu (x) (2-- for in some interval L. Determine L so that ,, is conjugate with Qμ
2 er Let I be an interval of R, and define the function f :I→ R by f(x) 1 +e2z or every z EZ. (a) Find the largest interval T where f is strictly increasing. (b) For this interval Z, determine the range f(T) (c) Let T- f(I). Show that the function f : I -» T is injective and surjective. (d) Determine the inverse function f-i : T → 1. (e) Verify that (fo f-1)()-y for every y E...
Problem 6. Let Coo(R) denote the vector space of functions f : R → R such that f is infinitely differentiable. Define a function T: C (RCo0 (R) by Tf-f -f" a) Prove that T is a linear map b) Find a two-dimensional subspace of null(T).
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1. Let Q1 , Q2, Q3, Q4 be constants so that f(z) = z4 + Qiz? + Q2z? + Q32+ Q4 is the characteristic polynomial of the matrix 42 1576 9 15 21-58 19 A76 -58 234 80 L9 19 -80 201J Let Q = In(3 + IQ1 + 2lQal + 3IQal + 4IQal). Then T = 5sin"(100Q) satisfies:--(A) 2. Let Qi s Q2 S Qs S Q4 be the eigenvalues of the matrix A of Question...
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g(2)-3 realnumbers. The graph of its derivative, g'(z), g'(a) Also define the differentiable, odd function hz) on all real numbers. Some values of h(z) are given below 0 12 3 4 5 h(z 02-42 2 (a) Calculate each of the following quantities or, if there isn't enough information, explain why i. (g'(x) +2) dr i.h() da ii. (h'(z) +2z) dr iv. 8h(x) dr...
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1 < p. Show that the conjugate is where 1/p+1/g-1
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1
4. Let G : P(R) → P2(R) be a linear map given by G(u)(x) = (x + 1)u'r) - ur). Is G diagonalizable? If it is, find a basis of P(R) in which G is represented by a diagonal matrix 5. Let V = P2(C). Show that the operator (.) given by (u, v) = u(0) v(0) + u(1) v(1) + u(2) v(2) Vu, v E V is an inner product on V.
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2. Let h : R-+ R be the smooth function given by h(z) g is as in Problem 1 g(z + 2g(2-x) for all r E R, where (a) Show that if a < -2 0 g(2) if -2< <-1 h(x) if 2 0 (b) Use part (d) of Proble 1 to show that for all E 0,9 in fact for all ,. Conclude that for all e 0,1 The functions from...