4. Show that the norm on (° given by I| (21, ..., In...) |lo= sup{|7;| : j =1,2, ...} %3D can not be given by a scalar product.

Q: u(x, 0) = ÷(1 -), 0 0 Eq. 2 Uz = a?uxx, 0 0 Eq. 3

A: Using superposition principle and half range Fourier series coefficients.

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dx X…

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Q: o limr→0 3 - Vx +9

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Q: Solve the initial value problem. dy =x*(y - 2), y(0) = 9 dx 囚 The solution is (Type an implicit…

A: To solve the initial value problem.

Q: Σ 2n n? + 2n h= 1

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Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: A graph of y = f(x) is shown and a c-value is given. Use the graph to find the following, whenever…

A: The given graph is     To find: (a) limx→c fx             (b) f(c).

Q: The inverse of matrix A is given. A-1 = Use the inverse to solve for X. Ax - Li]

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Q: Q4 (а) Identify the homogeneity of the following second order differential equation and state the…

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Q: 1. Obtain the PCNF and PDNF of the following proposition: (p – (q ar)) ^ (~p → (~q ^ ~r)) without…

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Q: Find the Sof (x, y,z)dV A. Q = {(x, y, z)|(x+y² +z 4 and z = x+y, f(x,y2) = x+y} B. Q= {(x, y, z) (x…

A: We will use the basic knowledge of integral calculus to answer this question correctly and…

Q: Octal numbers are made using the eight digits 0,1,2,3,4,5,6,7. How many octal numbers are 4 digits…

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Q: Find the direction in which f(x,y) = x²e-2y increases and decreases most rapidly at Po(1,0) and find…

A: Consider the given function, fx,y=x2e-2y Here we need to find the direction in which the function…

Q: Show that the equation + 2x- + (1- y²) dx2 dx²y dy? 2 is elliptic for values of x and in the region…

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Q: . Find the odd and even half range expansion of the given function: Hint: Use Slope Intercept Form…

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Q: Which of the following is simply connected? a) the horizontal strip Imz <1 b) the annulus 1</z <2 c)…

A: This is a problem of topology.

Q: The expression m(m-1)a, +x> ka,x is equivalent to the sum whose generic N=2 k=1 term involves x" is…

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Q: Find the eigenvalues A1 < A2 and associated orthonormal eigenvectors of the symmetric matrix [3 0 1…

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Q: 1. Let l: R2 → R³, l : x+ Ax, where k k %3D 2k –1 9 a.) Establish for which value of k, the linear…

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Q: dy -4 Given a differential equation with the initial condition, y :2. dx y cos (2x) (a) State the…

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Q: Let R be a ring such that for each a e R there exists XE R such that a'x = a. Prove the following :…

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Q: Consider a 25-year mortgage of $100,000 at 6.6% iterest compounded mortvy where the an i interet…

A: We can solve this using given information

Q: For the following exercises, determine a definite integral that represents the area. 198.Region…

A: We have to find the area of the region common to r=3 sinθ and r=2-sinθ

Q: dy dx y cos (2x) -4 Given a differential equation with the initial condition, y = 2. (a) State the…

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Q: Fer Me fellany geoph fue dlal

A: We will use the basic knowledge of graph theory to answer this question completely and correctly.

Q: Exercise 5 a) Given the differential equation y' + 3y = 0,9x. %3D Find A and B so that y = Ax+B is a…

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Q: 0, ts2 2 6

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Q: c) Mr Jason deposited $5000 into an account paying 6% annual interest compounded monthly, how long…

A: Solution :-

Q: 14-y2 구~ X 3 dy XP

A:

Q: The rectangle M, lies in the (x, y) plane in the (x, y, z) space, and is given by: M1 = { (x,y) |0<x…

A:

Q: At 3:01P.M, a thermometer reading is 90°C is taken outside where the air temperature is -10°C. At…

A: Given: Timing Thermometer Reading  Temperature 1:01 PM 90oC -10oC (Outdoor) 1:03 PM 36oC…

Q: (*) 3. Let 2 = {A, |n = 1, 2, 3, ...}, where A, Find UN and N2, then !! %3D prove your conjecture.

A: We solve this problem using the basic properties of union and intersection. Also some basic steps of…

Q: Solve the system +x2 +3x3 1 | 3x1 +2x2 -3x3 3 x2 +s 3.

A:

Q: Problem 1. Let (X, dx), (Y, dy) be metric spaces, and equip R with its usual absolute value-metric.…

A: Given: Let us consider the given,X,dX,Y,dY a) Let us determine the sequence of functions fn:ℝ→ℝ b)…

Q: f(t) = 3e7t - 3 cos(3t) + t?e-4t + 6.

A: Given  f(t) = 3e7t - 3cos(3t) + t2e-4t + 6    Results:  1) Laplace transformation is linear  2)…

Q: C(x) = = 60 + x² dollars. (a) Find the marginal cost at x = 4 units. MC(4) %3D Tell what this…

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Q: 12 n 12 n+ 3.64 2 n converges to The sequence an = Note: You may need to use the command.evalf() to…

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Q: 4. Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem:…

A: For (a), We are given the following initial value problem.       dydx+3x2y=6x2;  y(0)=3   -----(1)…

Q: Solve two of the three integrals -* xsin(x) ,x² + 25 20 xsin(x) de 5 + 4 cos(0) -dx (x2 — 2х + 2)2

A: Given ∫-∞∞xsinxx2+25dx Consider ∫Czsinzz2+25dz=∫Cfzdz Where C is a contour consisting of the…

Q: Exercise 4 Given the double integral: 2 |e** dxdy. a) Make a figure showing the integration area of…

A: From the given integration, it is observed that the region of integration is bounded by the curves…

Q: (b.) Consider the ordinary differential equation in (t > 0) ty" – (t+1)y' + y =0 Note that Y1(t) =…

A: The given ordinary differential equation is ty''-(t+1)y'+y=0...................(1) Write…

Q: define the region bounded by y = 0, y = 4√x, y = 24 − 2x, and y = x − 4 using vertical and…

A: Given curves are y=0, y=4x, y=24-2x and y=x-4. We have to define the region bounded by the given…

Q: 5. Sketch the graph of a function f with domain [1, 5] satisfying all the following conditions:…

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Q: The time period of the motion u" +192u =0 is a) T = 0.45345 b) T = 0.5345 c) T = 0.54345 d) T =…

A: We can solve this by given information

Q: how that in D4 is not a normal subgroup. Please explain in details and show all the works.

A: To Show, a subgroup in D4 is not normal.

Q: Convert the following diffrential equation into an integral equation : d'y + Axy = f(x), y(0) = 1,…

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Q: Show that the equation dy + 2k possesses solutions of the form 00 - kt E c,e cos (oa,x+ E,) cos (w,…

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Q: Jenck's Homemade Ice Cream, LLC is planning its production for next week. As there is a current…

A: We have to find the number of gallons of chocolate chocolate-chip ice cream and the number of…

Q: Derivatives of Algebraic Functions Directions: Prove the following statements. 13x + 20x* 2Vx3 +2…

A: Using the product rule of derivative, it can be written that: f·g'=f '·g+f·g'.

Q: Let p be a prime and let a ∈ Fp \{0}. Prove that the Galois group of f(x) = xp − x +a over Fp is…

A: