Chapter 8.6, Problem 4E

Pls help ASAP

Pls help ASAP

1. If f(x)=x²-5 and g(x)=5-x³, determine a simplified equation for h(x) = f(x)g(x).

Pls help ASAP

Pls help ASAP

Question 1. Prove that the function f(x) = 2; f: (2,3] → R, is not uniformly continuous on (2,3].

Consider the cones K = = {(x1, x2, x3) | € R³ : X3 ≥√√√2x² + 3x² M = = {(21,22,23) (x1, x2, x3) Є R³: x3 > + 2 3 Prove that M = K*. Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix A.

I am unable to solve part b.

Let M = M₁U M₂ UM3 and K M₁ = {(x1, x2) ER²: 2 ≤ x ≤ 8, 2≤ x ≤8}, M₂ = {(x1, x2)™ € R² : 4 ≤ x₁ ≤ 6, 0 ≤ x2 ≤ 10}, M3 = {(x1, x2) Є R²: 0 ≤ x₁ ≤ 10, 4≤ x ≤ 6}, ¯ = cone {(1, 2), (1,3)†} ≤ R². (a) Determine the set E(M,K) of efficient points of M with respect to K. (b) Determine the set P(M, K) of properly efficient points of M with respect to K.