8. Show that for any orthonormal sequence F in a separable Hilbert space H there is a total orthonormal sequence ♬ which contains F.

Q: Solve the following system of nonlinear equations 2x₁x₂2=0 x₁² - 4x₂ -4 = 0 Using the fixed-point…

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Q: 2. Using (a) Jacobi Iterative Method and (b) Gauss-Seidel Method, obtain the solution to [12x₂ + 3x₂…

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Q: If K is a field and if 1, 2 are distinct automorphisms of K, ther it is impossible to find elements…

A: This is a problem of Abstract Alhebra.

Q: (14). Obtain using Jacob's method, all the eigen values and eigen vectors of the following matrices:…

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Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: We will find equation of surface bounding the region of integral from its limits and then draw…

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

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Q: The following data define the sea-level concentration of dissolved oxygen for fresh water as a…

A: We can solve this using given information

Q: 1. Let z, y ER" be given. (a) If ||z||||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and…

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

Q: 2. Determining whether odd or even function, state the period. a.) b.) .

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Q: Which of the following shows the correct substitution of the variable u into the integral S₁ x√3x -…

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Q: 4. Show that for any bounded linear operator T on H, the operators T₁=1/√(T+T*) and T₁=1 (1 ==…

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Q: Example 11.1. Classify the following equations : au a²u d²u du (i) +4 0x2 +4 Əxdy 2 ông Ôx ди +2- =…

A: Given the second order partial derivatives; ∂2u∂x2+4∂2u∂x∂y+4∂2u∂y2-∂u∂x+2∂u∂y=0…

Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

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Q: Example 10.12. Solve the following by Euler's modified method dy = log (x + y), y (0) = 2 dx. at x =…

A: Solution: Given, y'=log(x+y) y(0)=2 Applying Modified Euler method: f(x,y)=log(x+y)…

Q: dy Example 10.24. If dx mula by calculating y(1), y(2) and y(3) using Euler's modified formula. = 2e…

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Q: 3. A loan of 7 quarterly payments of Php.8,300 is to be made, to pay for a loan at 10% compounded…

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Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 26 p44 dxdy xy A

A: FIND THE integral value USING SIMPSON RULE

Q: 1/3 y = x¹, x = 0, y = 1; about y = 2

A: As per the question we are given a solid of revolution which is obtained by rotating the area…

Q: By using the method of least squares, find the best line through the points: (2,-3), (-2,0), (1,-1).…

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Q: Use separation of variables to find a product solution to the following ди ди = дх ду И=c - (;) Pu=q…

A: Partial differential equation is a differential equation in which there is one independent variable…

Q: Let D be the portion of z = 2z + 5y inside z2 + y² = 1, oriented up, and let F = (y, z, -z). Compute…

A: Solution :  Options ( 3 )  is correct

Q: . Show that d(w) cos(Kt). = π[d(w − K) + d(w + K)] is the Fourier transform of -

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Q: The real part of csch (2-j3) is O -0.5118 O none of the other choices O -3.5906 O 9.8844 O 1.0357 O…

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Q: Use the "Big Idea" of transformations to find equations for these two functions. 1.1 Unsaved 1.1…

A: As per company guidance i am solving first question please resubmit for another one. Consider the…

Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

A: Solution. :

Q: g(x) x-0 /(x) Evaluate lim . . . " . . .. . * . . . . . . 4 . . . * * + + * . . . . * . . . . f(x)…

A: Solution : To find, limx→0g(x)f(x) Given,  From graph , f(x) is a straight line passing through…

Q: Example 9.16. A light elastic string stretched between two fixed nails 120 cm apart, carries 11…

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Q: The rate of change of the height h(t) of water in a cylindrical tank with a hole in the bottom is…

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Q: ( Minimize z = (x₁ − 4)² + (x₂-4)² subject to 2x₁ + 3x₂ ≥ 6 -3x1-2x2 ≥-12 x₂20;x₂20

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Q: 1.Tony is 6 years older than Jonathan. Six years ago, she was twice as old as he. How old is Tony?…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: . Determine the volume of the solid obtained by rotating the region bounded by y= x - x^3, x = 0, x…

A: Solution :

Q: Let D be the portion of z = 2z + 5y inside z² + y² = 1, oriented up, and let F = (y, z, -z). Compute…

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Q: C:1: Solve the following I.V.P. using Laplace transformation: y" - 2y - 5y = 5t-100 such that: y…

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Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: Example 10.17. Apply Runge-Kutta method to find approximate value of y for x = 0.2 in steps of 0.1,.…

A: Probem is solved using runge kutta method.

Q: Example 10.22. Using Runge-Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that dy/dx =…

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Q: p(1U1) and p((2U2) 1)). 0.11 0.05 0.07 0.08 0.09 0.10 0.20 0.12 0.15 1 0.03

A: Follow the steps.

Q: 2°) Write the volume integral of the solid bounded by 2 = √√√x² + y²² and == √√2-x²-y²², in a)…

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Q: 10. Let X be an inner product space and T: X→→→→→X an isometric linear operator. If dim X<∞, show…

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Q: Given that A and B is a group. Find out if : A→B is a homomorphism. If it is a homomorphism, also…

A: We have given a map ,  ϕ : A → B , where A = ℝ , +   ,  B = ℝ* , · such that  , ϕx = 2x We know that…

Q: Refer to image.

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: • Create a symmetric equation of a line with the digits 6, 8 and 4. Does the point D (7,-1,8) lie on…

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Q: In how many ways can 6 girls and 3 boys sit on a row of 9 chairs in such a way that no two boys sit…

A: we have to solve given problems:

Q: 5 6. (s+3)² 7. 3 s2-32 8. L{f(t)}: 3s²-1 s²+8+1

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Q: Example 10.37. The deflection of a beam is governed by the equation day +81y = o(x), where (x) is…

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Q: Suppose the functions f, g, h, r and I are defined as follows: f (x) = log+log x 3 g(x) √(x+3)² h(x)…

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Q: (i) Sketch the graph of y = cos x for 0° ≤ x ≤ 360°. On the same axes, sketch the graph of y = cos…

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Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

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Q: Which of the following is or is not an improper integral? Clearly explain your choice. A. ₂ dx B. dx…

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