. Consider the BVP d²u dr² ² cos(x), 0 < x < 1, u(0) = 1, u(1) = -1. Replacing the derivative with a central difference quotient and using 3 equally spaced nodes gives where u, U1 U₂ u(ih). Determine the 2 x 2 matrix A and 2 x 1 matrix b. A

Q: If u = 3x – x3 + 3xy? is a real part of an analytic function | f(z) = u + iv, where z = x+ iy is a…

A: Solution

Q: Are x, sin(x) and cox(x) linearly independent

A: True x, sin(x), cos(x) are linearly independent

Q: Prove that •1 to(xt) 1-1² dt = Sinx x

A:

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A:

Q: A. Find the second derivative of y=- (x+1)³ B. 4x x+1 (x+1)³ C. 8 (x+1)² D. (x+1)²

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Consider the function f(x) = ln(x2). Let L(x) be the local linearization of f aboutx bar = a.a) What…

A: General expression of local linearization of a function f(x) about x0 is given by,

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=sin(2x)+17 To find: f'π2 and f'(π)

Q: 12. ∇⋅F of F = (2xy2)i-(3y3z2)j at (2,1,-2). a. 4 b. 27 c. -7 d. -34

A:

Q: 2. Find a function f and a number a such that f(t) -dt = tanx. Give proper reasoning.

A:

Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

A: As per the policy of bartleby the provisions is to solve only one question at a time  I am solving…

Q: 4) Determine the function F(x)=[ƒ(1)dt, where ƒ(x)=sgn(x-x²) for xe[-1,2]. -1

A: f(x) is discontinuous but F(x) is continuous

Q: [2 0 -1 2 1] В — -1 1. Let A 3 1 [1 2 D = C = E = -1

A: DA  = 21112310-12        = 2×2+1×0  2×3-1×1  2×1+1×21×2+1×0  1×3-1×1  1×1+1×2        = 454223 (DA)'…

Q: Find the value of a,b ∈ R ,so that the following sets of functions are linearly independent for all…

A:

Q: Consider the linear model: ky = xy +e E(e|x) = 0 where k is a known positive scalar. Cov(A,B) (a)…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

A:

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

A:

Q: 10. Let V be the vector space of functions spanned by B = {cos x – sin a, cos a + sin æ}. Find the…

A:

Q: Let h(x) be given by the graph. (a). List all of the zeros of h(x). For each zero, determine if it…

A:

Q: For convenience, we write the coefficients uj,¿ in the vector {u} = (u₁, U₂,. where l - 1 + i + (N +…

A:

Q: 1. Use the "First Fundamental Theorem Of Calculus" to find the first derivative of the function. 2 –…

A:

Q: (2) The derivative of r at the попzеrо real nuтвer a is Dr.(h) = -h/a². Proof. (1) Compute, p(a + h,…

A:

Q: Solve the first-order linear ODE t(t + 1)x' + tx = 6.

A:

Q: Show that the function f(x) = x’ + 1 is invertible from R to R.

A: First prove that the  function is one -one  let f(x)=fyx7+1=y7+1x7=y7x=y therefore, the function is…

Q: Find a linear differential operator (of lowest order) that annihilates the given function: f (x) =…

A:

Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: Let g'(x) 0. B. g(1) = - 3, g(7) = 1, g(15) = 10 1 C. g(1) = 1, g(7) = 7, g(15) = 14 D. g(1) = 10,…

A: