Which of the following functions are one-to-one?

Group of answer choices

f;[−3,3]→[0,3],f(x)=9−x2f;[−3,3]→[0,3],f(x)=9−x2

f;R→R,f(x)=x3f;R→R,f(x)=x3

f;[0,∞]→[0,∞],f(x)=x2f;[0,∞]→[0,∞],f(x)=x2

Please provide proofs for parts i.)-iii.)

(i) Refer to the sequence in 1(ii). Show that with respect to the supremum norm on ?[0,1] this is a bounded sequence that has no convergent subsequence. (hint: What is the value of ‖?? − ??‖∞ if ? ≠ ??)

(ii) Refer to the sequence in 1(v). Show that this is a bounded sequence with respect to the 1-norm on ?[0,1] that has no convergent subsequence.

(iii) Let ℎ?(?) = sin??. Show that with respect to the 2-norm ?[0,2?], (ℎ?) is a bounded sequence that has no convergent subsequence. (This exercise shows that the Bolzano-Weierstrass Theorem does not generalise to ?[?,?] with any of the 3 “natural” norms on ?[?,?])

Note: sequences from 1ii.) and 1v.) are pointwise functions and are defined respectively below:

1ii.) For ? ≥ 2, define the function ?? on [0,1] by: ??(?) =( ??, if 0 ≤ ? ≤ 1/?)

(2-??, if 1/?< ? ≤ 2/n)

(0, if 2/?< ? ≤ 1)

1v.) Hn=n?? (and fn is defined as above)

Compute the Taylor series at x = 0 for ln(1+x) and for x cos x by repeatedly differentiating the function. Find the radii of convergence of the associated series.

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x).

For each of the following statements, prove or disprove the statement.

(a) For all relations R on X, if R is reflexive then S is reflexive.

(b) For all relations R on X, if S is reflexive then R is reflexive.

(c) For all relations R on X, if R is symmetric then S is symmetric.

(d) For all relations R on X, if S is symmetric then R is symmetric.

Chapter 9 discussed the importance of stakeholder engagement in policy making. The author presented several benefits and an analysis of five cases in which stakeholder engagement added value to the policy making process. If you were leading a project to develop a comprehensive policy for managing pedestrian traffic flow in a popular downtown metropolitan district, what measures would you take to engage stakeholders in that project? Your answer should outline your suggestions and clearly explain why each one would add value.

Need 300 words with no plagrism

. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t) = 5e^3t cos(4t) − 6e^2t sin(7t)

Sports Finance Questions

1. Compare and contrast various segments within the sport industry and how they handle financial issues.

2. Examine how sports facilities can become an economic engine for revenue generation.

3. Forecast the future of the sport industry based on changes in the sports broadcasting field.

Find a particular solution of

y'' + 2y' + y = e^-x [ ( 5 −2x )cos(x) − ( 3 + 3x )sin(x) ]

y_{p( x ) = ?}

_{Please show your work step by step. Thank you!}

1. A round column is to be designed with DL = 600 KN, LL = 800 KN, fc’ = 20.7 MPa, fy = 345 MPa. Use ?? = 0.02, 25 ?? ∅ ???? ????, ??? 10 ?? ∅ ???. USE 1.2 DL + 1.6 LL USD AND WSD. provide detailing

Students will be asked to formulate, define, and interpret mathematical modeling (particularly ordinary differential equation) which involves real engineering applications and related to their majoring (E.g. Newton’s law cooling/warming, mixture problem, radioactive decay, spring-mass system, series circuit, deflection of the beam, etc.).. The selected model should be solved analytically using any methods that have been learnt in the mathematic lecture. just give me an example with related topic and how to solve it using math

5)   Solve 2yy’’ = 1 + (y’)^2

Consider ỹ + cỷ +y = 0, and assume y(0) = 1, ÿ(0) = 0. (a) Why is this a homogeneous system?
(b) What would change if this was to be an inhomogeneous system? When is this inhomogeneous aspect applied - this is a technical point, but helps us to understand that the initial condition is an external input too, but is *only* applied at t = 0?
(c) Choose e to make this problem overdamped/critically damped/underdamped.
(d) Follow the 3-step procedure to solve this homogeneous system for the ho- Imogeneous solution y which we call y: Step 1: Get yh. Step 2: Satisfy condition, and Step 3: Sketch. • Solve the overdamped case where c is the critically damped version where c is increased by 1 past the critically damped value. Solve the critically damped case, • Solve the underdamped case where e is the critically damped version where c is reduced by 1 below the critically damped value.

1)Prove that the intersection of an arbitrary collection of closed sets is closed.

2)Prove that the union of a finite collection of closed sets is closed