Prove the following statement: For any function f : R" - R and any function g : R" R, let h: R" R be defined as h(x) = max{f(x), g(x)} at each x e R". If f and g are convex functions then h is also a convex %3D function.

Q: f(t) = (1 + tet)*

A:

Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

A:

Q: 2. Assuming chop arithmetic with b = 10 and m = 4. Sum the numbers 999.9 + 99.99 + 9.999, from left ...

A: We want to sum 999.9 + 99.99 + 9.999 Here b=10 and m =4

Q: The commutator [X. Y] of two matrices is defined by the equation [X. Y] = XY YX. Two anticommuting m...

A:

Q: PROBLEM: lim CSch 2 ATTEMPT: CSch csch x In %3D Ix1 _csch x = In I+ (0)= In ! (히 %3D In Ito 4. 101 1...

A:

Q: State A and state B are each candidates for an extra congressional representative. The relative unfa...

A: Relative unfairness = absolute unfairnesssmaller average constituency  

Q: Problem 1. Give an example of a normed space E and a convex function p:E - R such that p is not lowe...

A:

Q: Consider a dynamic system described by the following integro-differential equation 4x+3x+2x+5| x(t)d...

A:

Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

A:

Q: 2. Let N = {A, | ne N}, where A, = {n,n+ 1, n +2, ...}. (a) Find UN and prove your conjecture. (b) F...

A: we have given Ω = An n∈N where An =n, n+1, n+2,...... we have to find (a) find ∪Ω and prove your con...

Q: I ind the second derivative(y") of the following functions and simplify the final results. 1. y = x ...

A: Differentiate using the rules of derivative.

Q: find the measure of <1 243°

A:

Q: For integers n >1, 2 3 1 + 2! n 1 1- 3! 4! (n+ 1)! (n + 1)!

A: solving the problem using induction:

Q: f (x) = 7X 0< RくL 1<スc2

A:

Q: Integrate * 2+7 sin'z dz coz²z 2 cos z + 7 sin z + 7 cos z + C O 2 tan z + 7 sec z + 7 cos z + C Non...

A: We have to integrate:∫2+7sin3zcos2zdz=∫2cos2z+7sin3zcos2zdz

Q: Find the Fourier transform 1-x, | x | 1 sin x Cos X CoS x Hence evaluate dx.

A:

Q: List the eigenvalues of A. The transformation x-Ax is the composition of a rotation and a scaling. G...

A:

Q: Let G be a connected graph and e and edge of G. Prove that k(G) = k(G - e) + k(G/e). Here k(G) repre...

A: Given  G be a connected graph and e an edge of G  we have to prove that kG=kG-e+kG/e here k(G) repre...

Q: Consider the following inputs coefficient matrix: 0.25 0.4 0.2 A = 0.25 0.1 0.1 0.25 0.1 0.3 Find th...

A: Remark: The minor of an element in a matrix is the value of the determinant of the matrix that resul...

Q: How many tangent planes to the hyperboloid r-y?-2 1 are parallel to the plane z= r +y? %3D

A:

Q: () - -() n n Proposition 10. Let n and k be positive integers. Then k = n k k- 1 Special directions:...

A:

Q: y = c1z + c2e - 22 - z - 1 isa general solution of the differential equation Select one: O a (z – 1)...

A: Let us consider a differential equation f(x,y,y',y'',......)=Q(x) The equation y=f(x) is the general...

Q: Solve the differential equation y = x – 1+ xy – y.

A:

Q: T AppLiCATIONs 1. Schve for the orthogonal trayectories (a+x)y² = x*( 3a-x)

A: 1) solve for the orthogonal trajectories a+xy2=x23a-x                  ...i differentiate with respe...

Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order linear...

A:

Q: The graph below represent the domain of the function O f(r, y) In(1 -+y) Of(r, y, z) = VI+y-1 Of (r,...

A: The given graph represents x+y&gt;1. The domain of ln(1-x+y) is 1-x+y&gt;0⇒-x+y&gt;-1⇒x-y&lt;1. So t...

Q: 2) y" - 2xy' +y

A:

Q: Laplace transform

A:

Q: 4. Find the values of w, x, y, and z using Gauss-Jordan Elimination 1 5 -2| 7 3 2 0 |12 2 -2 0 3 5 -...

A: Since you have asked multiple questions, we can solve first question for you. If you want other ques...

Q: ) g"- (x+)g'-y -o =0

A:

Q: The curve C is the circle of radius 5 contained in the plane z 5 and centered around the z-axis, ori...

A: Solution:-

Q: I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. í. . SLALE.. 2. The ne...

A:

Q: Let f = ao+ajx+…+a„x" be a polynomial. I can treat f as an element of R[x] by defining an+1,&n+2,......

A:

Q: estion: 3 a) Solve the given initial value problem. x2 d-2xy = 3y*, y(1) =

A: The solution of the differential equation x2dydx-2xy=3y4 is defined as the function which satisfies ...

Q: Proposition 9. Let n be a non-negative integer. Then 1+2+4+ 8+ ...+ 2" = 2"+1 – 1.

A: see the attachments below

Q: 1 5. If the Laplace transform of f(t) = e %3D find F(4s)

A: Given that the Laplace transformation of f(t) = e^(1/s)/s. We have to find F(4s).

Q: 5. Provide a derivation for the following argument. You may use either basic or derived rules. Hint:...

A:

Q: Suppose a graph has vertices of degree 0, 2, 2, 3 and 9. How many edges does the graph have? Provide...

A:

Q: Proposition 7. Let a, b, c, d E Z and n be a positive integer. If a = b (mod n) andc = d (mod n), th...

A:

Q: 7. Produce the quadratic polynomial interpolating the data {(-2, -15), (-1, -8), (0, -3)}. Find the ...

A:

Q: 3pi Find the value of tan, - 2i, ( 4 一 13 j1490 355 1491 13 355 1490 13 355 1490 1491 13 355 1490

A:

Q: Find bases for the column space, the row space, and the null space of the matrix 3 -1 1 A =| 3 12 -1...

A:

Q: List the eigenvalues of A. The transformation xAx is the composition of a rotation and a scaling Giv...

A:

Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f(x) In(3 – 2.r) b) Fin...

A: Macluarin series expansion , interval of convergence 

Q: List the eigenvalues of A. The transformation x-Ax is the composition of a rotation and a scaling. G...

A:

Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

A:

Q: & Gier, Mamiten 3. - 2 -4 -6 12 15 3 -12 3 ID 2. ーC 4 6. 4 15 4x 5 5x3 No.of Column A No.of mws in B...

A:

Q: u(x, y) be a harmonic function in a domain S. Show that 18.5. Let u = all partial derivatives ur, y,...

A: If u is harmonic then it satisfies laplace equation. 

Q: may only use methods shown in class. 1.) Use the graph of f(x) below to evaluate the following: b.) ...

A: The limit of the function at x=a is the value of the function f(x) as x approaches to a The limit of...