1 3 uz (0, t) = uz (π, t) = 0, ux Ux 10x U t = - U x x u(x, 0) = ㅠ 0 Σχ Σπ

Q: [3] 37 Let A = Write 2A. Is det(2A) equal to 2det(A)?

A:

Q: I х F(x) 1 2 8 3 27 и ви

A: We are given the following question,   In this we need to solve the subparts- To estimate f(3.5)…

Q: Suppose q is directly proportional to the square root of h and inversely proportional to the cube of…

A:

Q: Consider the function f(x) = −5x² + 70x + 6 on the interval [-3, 9]. Find the absolute extrema for…

A: The given problem is to find the absolute maximum and absolute minimum of the given function over…

Q: Find the Laplace transform of the following function. That is, determine coefficient G f(t) = 6e F…

A:

Q: 2. LEFT AND RIGHT LIMITS (a) Prove that f: (0, 1)→ R defined by f(x) = = is not uniformly…

A:

Q: Consider the function ƒ(x, y) = x² + 2xy − 6x + y² − 6y + 9. In the box below, enter the maximum…

A: The maximum rate of change at any point (x,y)∈D(f) is the magnitude of the gradient at (x,y),…

Q: Find the Laplace transform of the following function. That is, determine coefficient I f(t) = 6e-5t…

A: Solution is given below:

Q: Suppose f(n) = 9n² 16n + 42(log(n))² and g(n) = 4n². Using the formal definition of Big- O, prove…

A: First of all, let        h(n) = log(n) - n + 1    => h'(n) = 1/n - 1 < 0 for all n > 1…

Q: Graph the inequality. x > 3y

A: Given inequality is x > 3y

Q: Let X₁,..., Xn,... (a) Prove that SA (X) = (X₂)² is consistent for . (b) Prove that dB(X) = (X₂)² -…

A: (a) To show that SA(X) = (Xn)² is consistent for , we need to show that SA(X) converges in…

Q: (1) R₁0 R₁ (m) R₁0 R₁ (n) R₁0 R₁

A:

Q: a. a d g -3b - 3e -3h b c e f h i -a b. -d -g 3c + x b 3f+y e 3i+z h

A:

Q: 4 6. This rectangle of x's is of another (original) rectangle of x's. X X X X X X X X X X X X X X X…

A: The given rectangle is 45 of original rectangle which means 45 of number of X's in the original…

Q: If p, q, r are prime numbers such that p = 19(p + q + r) then the value of 2(p + q + r) is

A:

Q: Use the simplex method. Minimize g = 10x + 9y + 11z subject to x + y + z 2 3 y + 2z 22 x 22. (x, y,…

A: To Solve: Min g=10x+9y+11z  subject to x+y+z≥3 y+2z≥2 x≥2 Using Simplex-method.

Q: Problem. Let F be a fixed n x n matrix and define a function T: Mnxn →Mnxn by T(X) = FX - XF. •…

A:

Q: Let H = {A € R³×3 | A is not invertible}. Show that H is not a subspace of the vector space IR³×3.…

A:

Q: Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A= E The determinant…

A: The given matrix is  A=abcd, E=1k01 We have to verify detEA=det EdetA. Also, aij=a11a12a21a22 We…

Q: Find a linearization at a suitably chosen integer near a at which the given function and its d are…

A:

Q: 6. Find the matrix A such that: (question continued on the next page) 433 253 657 1 2 2 20 -3 1 A 1…

A:

Q: let x = { a, b, c, d, e} T = ($₁ {a,b,c}, { lide}, {C}₂x} be a toponx is G = { a, b, c, d Connected…

A:

Q: 2.1 DEFINITION OF THE LIMIT OF A FUNCTION x²-4 -4 x+2 2x² + 3x - 2 x+2 1. Define f: (-2, 0)→ R by…

A:

Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

A:

Q: Consider the region bounded by y = x and y = 4√√x. (a) Draw a clear picture of this region including…

A:

Q: College of Letters and Science, the College of Fine Arts, the School of Business Administration, and…

A:

Q: Question #8 - A retail outlet sells 2000 pairs of pants a year. It costs $2 to store a pair of pants…

A:

Q: The graph shows a rough representation of the (aggregate) market depth† of the stocks comprising the…

A: The graph shows a rough representation of the (aggregate) market depth† of the stocks comprising the…

Q: u = [3, -4] and v = [6, k], what is the value of k if u is orthogonal to v?

A:

Q: Define the students enrolled in this class during this semester as a set, S. a. Specify a partition…

A: Let S be the set of students enrolled in this class during this semester. a) Then, consider the…

Q: Find vectors v, w R³ such that v+w= (1,3,7), v is parallel to (1,0,1), 2. and wis orthogonal to (1,…

A:

Q: 3 Using matrix diagonalisation, solve the following system of first order difference equations: Xn+1…

A:

Q: 4 Suppose that firms in a particular industry fall into one of three size categories: large, medium…

A:

Q: The least squares fit line for the points (3, 3.1), (2, 2.3), and (1, 2.1) has form y = mx + b.…

A: Given: It is given that the least squares fit line for the points 3, 3.1, 2, 2.3, and 1, 2.1 has…

Q: 1. Find the equation of the tangent plane for the implicitly defined surface xy + xz+yz = 1

A: First we arrange the equation of the surface into the form  f(x,y,z)=0 xy+xz+yz-1=0

Q: Hetermine a region of the ty-plane so differential equation has a unique sol

A:

Q: Let U be an open subset of R2, 0 EU, f: UR be a differentiable function, and Vƒ(0,0) = (0,0). Let S…

A:

Q: Solve the initial value problem. dy y =xẻ, y(1) = e + 3 dx X The solution is y(x) =

A:

Q: Consider f(x) = 3 x . Describe how the graph of each function compares to f. 8. g(x) = 3 x + 4 9.…

A: Sol:- For each of the given functions, we can compare the graph to the graph of f(x) = 3x by…

Q: 2. Recall that the Fibonacci sequence a1, a2, a3,... is defined by a₁ = a₂ = 1 and an = an-1 + An-2…

A: The Fibonacci sequence an is defined by a1=a2=1 and an=an-1+an-2    ∀n≥3.       We know for two…

Q: (a) (b) Show that the equation x+y+z+sin(xyz) = 0 defines z as a function of x and y in a…

A: Given: Equation: x+y+z+sinxyz=0a) We need to show that given equation defines z is a function of x…

Q: 1 For each of the following systems of equations, write down the coefficient matrix A and the…

A: 1. (a) The given system of linear equation is  2x-y+z=54x+2y+z=4-2x+y+2z=1   ⇒2-11421-212xyz=541.

Q: 8) Find a unit vector in the direction that f(x, y, z)=2x² +6xz²-yz³ increases most rapidly at the…

A: Given: A function fx , y , z=2x2+6xz2-yz3. To Find: Unit vector in the direction of the given…

Q: A tank initially contains 50 gal of pure water. A solution containing 2 lb/gal of salt is pumped…

A:

Q: Formulate a problem that would have the following generating function way to find a solution.…

A: Given: The generating function: 1+x+x21+x2+x4+x6x+x3+x5+x7+……….We need to formulate a problem that…

Q: What is Im (i (3 + 2i) (7 +5i))?

A: Given that the complex number Imi3+2i7+5i   .

Q: Find the flux of the vector field  V(x, y, z) = 3xy2i + 3x2yj + z3k out of the unit sphere. Use the…

A: Sol:- The surface integral of a vector field V over a closed surface S is given by: ∬SV.dS=∫∫∫V.n dV…

Q: 5. Evaluate the following. (b) 1²y² lim (y)+(0,0) + 3y fryz (T, y, z) if f(x, y, z) = (ry +zz+yz)²

A:

Q: 3. For this question you should use the fact (given on Assn.4) that the matrix -3 6 6 4-5 1 4 2 8-9…

A: (a)  From given data the linear transformation T : R6→R4 defined as  T(x) = Ax       where  A=…

Q: For a 3-year term insurance on (a), you are given: i. The death benefit is 1000 payable at the…

A: To approximate the expected present value of insurance benefit using the claims acceleration…