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

Q: Find the rectangular form of 3/2 et* i.e. the a + bi form.

A:

Q: ř(-1)n+12nx" n² + 3 n=1

A:

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y ...

A: Please see the attachment

Q: (4) Let A E R™xn be any matrix. Solve the following problem min ||AX – I||r Hint: Write X = [x1,...,...

A:

Q: If X = {1,3,4,15}, Y = {2,3,4,7} and Z = {2,4,6,9}, then what is X U (Y N Z)? а. {2,4) b. {4} c. {1,...

A:

Q: [x² when x # 1 9: Show that f(x) = %3D 2 when x =1 is discontinuous at x = 3D1

A: The given function is: f(x)=x2when x≠12when x=1We have to show that the given function is discontinu...

Q: Solve the IVP for y(æ): dy + dr y = 19y", y(1) = 1 y(z) =

A:

Q: Solve the following ODE using Laplace Transforms Method: y'+y=2sinx when y(0) = -1

A:

Q: /|| (x + y + z) dV, where E is the solid in the first octant that lies under the paraboloid z = 16 –...

A: see the attachments below

Q: 1. Find the Fourier transform of f(t) defined by: 0 t<0 e-6t t20 f(t A. (6- jw)/(36+ w^2) B. (6 + ja...

A: Fourier transform of the pice wise function

Q: Find at (2, -2, 1) if dy x2 + y? + 22 = 6xz + 6yz + 21 %3D

A: Given that x2+y2+z2=6xz+6yz+21 Then we have to find ∂z∂y

Q: Find bases for the column space, the row space, and the null space of the matrix 1 3 -1 11 A 3 12 3 ...

A:

Q: 3. Convert each of the following to exponential form and solve. a. n = log,16384 b. 6 = log,46656 %3...

A:

Q: Convert the given mathematical expressions into its corresponding C++ language expression using the ...

A:

Q: Suit Sales The number of suits sold per day at a retail store is shown in the table, with the corres...

A:

Q: 9. Obtain the shortest distance and shortest path from vertex 1 to every other vertex in the network...

A: To find the shortest distance between the vertex 1 to every other vertex .  

Q: List the eigenvalues of A. The transformation XHAX composition of a rotation and a scaling. Give the...

A: This is a problem of linear transformation.

Q: Find the area inside the larger loop and outside the smaller loop of the curve + sin(0) 2

A: To find the area inside the larger loop and outside the smaller loop of the below curve. r=12+sinθ

Q: Laplace Transformation

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:

Q: Calculate the order of the local truncation error of the Crank-Nicolson method for approximating the...

A: We are given the heat equation as ∂u∂t-∂2u∂x2=0. Now, we will be approximating the heat equation by ...

Q: y У — х. y' = 2+ sin

A: Given y' = yx + siny-xx    ---(1)

Q: Find the derivative of the function by quotient rule. f(x) = 3x+7 5х-2

A: Use the quotient rule to differentiate the given function as in next step.

Q: If we multiply a row in a matrix A by a real number r, JAl changes in r.

A:

Q: Proposition 8. Let m be any integer. If 5|(7m), then 5|m. Special directions: You can not use your p...

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: 1. For numbers 1 to 3, refer to the given problem. Xinggiu is reading a novel he bought from the boo...

A:

Q: Given this periodic function: f(t) =1 from 0<t<a and f(t) = 0 from a <t< 2a Solve for the Laplace tr...

A: Please find attachment for the details solution 

Q: Solve the differential equation (D3 – D² – 4)y = 2x2 – 4x – 1+ 2x?e2x + 5xe2x + e2x

A:

Q: Q6/ Find the moment of inertia and radius of gyration about the x-axis of a thin plate bounded by th...

A:

Q: Assume that x x(t) and y y(t). Let yx +1 and dx 2 when x 3 dt dy when x 3. dt Find

A:

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

A:

Q: QUAD is a rectangle, if 25 = 53 find Z1

A: A rectangle is a quadrilateral, such that all angles are perpendicular and opposite angles are equal...

Q: Prove the following logical equivalence by using a sequence of justified logical equivalences (indic...

A:

Q: ſcos 3t sin 8t dt * 1/2 (-1/5 cos5t - 1/11 cos11t ) + C O 1/2 (1/5 cos5t - 1/11 cos11t) + C O None o...

A:

Q: What is the missing length? 4 km 14 km area = 91 km? kilometers Submit

A: We know that the area of trapezium is: A=12(a+b)h    ..........(1)where,a and b are the length of th...

Q: How many vertices do the following graphs have if they contains a) 16 edges and all vertices of degr...

A:

Q: Proposition 11. Let ao = -1, a1 = 1 and a, = 7an-1– 10an-2 for integers n > 2. Then the closed form ...

A:

Q: Prove that for any integer n, we have n - 2 is not divisible by 4.

A:

Q: Which is an example of a veto power voting system? {4: 1, 1, 1, 1} {27: 3, 5, 9, 6, 4} {34: 13, 9, 5...

A: In the veto power voting system one with veto power can veto the decision of all other voters by his...

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y ...

A:

Q: 2 0 1 8] 5 6 0.5 3 [20 A = |-5 [24 12 -36] 10 -30] 5 [2] B = |1 C = [0 8 4] D 2 1 2 4 Lo] -3 7 –1 0]...

A: Please find attachment for the details solution 

Q: V Solve using method of undetermined coeficents (D³+GD°+ 12D + 8)y =o when x=0, y=1, y'=-2, y"

A:

Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y)...

A:

Q: The equation H (t) = a cos (bt) + d can represent this scenario. Identity the values of a, b and d. ...

A: Transformations of sine and cosine function

Q: 5. f (t) sinh 3t + cosh 3t – 2t3

A: This is a problem Laplace Transform.

Q: Find an equation for the graph shown below. (Hint: use the form y = a(x – h)? + k) -6 -5 -4 -3 -2 -1...

A:

Q: 7. Read about the Integral Test in Section 11.3 and, specifically, through example 2 to see how 1 th...

A: Series and sequences, integral test

Q: the following dineor sytam of linear matiz faderiation lwe egs using 2x. + X4

A:

Q: 5. Consider the false statement Vr, y E Q, x < y = A counterexample is a = -1 and y = -2.

A: