Show that the finite difference formula 1 Dzu(î) = [Зи (т) — 4u(г — h) + u(т — 2h)] 2h is a second-order approximation for u'(a).

Q: Verify that u(x, y) = x4−6x2y2+y4 is harmonic everywhere and determine its harmonic conjugate

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Q: (7) (a) Find the linear approximation L(x, y) to the function f(x, y) = √² + y² + 4 at the point…

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Q: 2. Derive an O(h4) five-point formula to approximate the second derivative f (xo) that uses f(xo –…

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Q: 16 Therefore f(x) = = co + C1x + c2x²+.. , where %3D x2 + 2x – 3 Co = C¡ = C2 = C3 =

A: given a function : f(x)=16x2+2x-3 We need to obtain it in the form of : c0+c1 x+c2 x2 + ... where c0…

Q: Show that the functions y₁= and y2 = 3. DE 4x²y" + 8xy' + y = 0. Show all work. In (x) √x form a…

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Q: Suppose = f(). (a) Given y(xo) = yo, when does this equation have a unique solution? (b) Make a…

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Q: Find some simple polynomials in (x, It) that satisfy the heat for XER²: equation Au = U Ди ихах, + и…

A: We  have  to  find  a  polynomial in where   such that that polynomial satifies     Suppose that…

Q: the error estimate for Taylor polyno

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Q: The function f(x) is invertible. Find (f-1)' (-8) given that f(x) = -x³ – 4x – 3.

A: f(x) = -x3-4x-3 We will use the formula for the derivative of the inverse function: f-1'x0=1f'(x0)…

Q: sy? is a real part z = x+ iy is a ce action v is

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Q: The value of Jo(0) + Jn(x) + J_n(x) is O a. 1+ J,(x) [1+ (-1)"] O b. J„(x) [1+ (-1)") Ос. 1-2J, (х)…

A: From bessels function results

Q: 1² cu (u + 4)(u - 5) du

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Q: 1. If f(x) = ax² +b where a and bare real constants, then show that (a) f[xx] = a (x₁+x). (b)…

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Q: Given a function f(x,y,z) = (x+3) In (6y - 4) sin (10z). Find the domain of the function. %3D а. (…

A: Domain - values of variables (x,y,z) for which the function is defined.

Q: 2. Find y' (a) by applying the Product Rule (b) by multiplying the factors to produce a sum of sim…

A: In this question, the concept of derivatives is applied. Derivatives We can use a derivative to…

Q: Suppose that F(x)=f(g(x)) and g(14)=2, g'(14)=5, f(14)-15, and f(2)=11. Find F(14). O 17 O 20 24 O…

A: Given query is to find indicated derivative

Q: Write the Linear Approximation to f(x, y) = x(1 + y)−¹ at (a, b) = (8, 1) in the form f(a+h,b+k)≈…

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Q: 3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b)…

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Q: that the Lagrange Polynomial of values Know follows b) F a) T as 0 1 2 = (x²-19x + 6) :- 3 7

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: Let z1 = -2 + 11i, z2 = 2 – i. Showing the details of your work, find, in the form x + iy: Re (zi).…

A: Here we can use following formula If z1=a+bi, z2=c+di,…

Q: 1 1 .3 x° + 3 1 Given the function f (x) = -x* – x2 a) Determine f'(x). Consider the function f (x)…

A: Dear student. You have posted many questions. According to the policy, we will answering the first…

Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

A: given  F''(x)=Ax+BF'(1)=r and  F(1)=sF'(x)=∫(Ax+B)dx∫xndx=xn+1n+1+c

Q: 1) Find the hundredth derivative of p (x) = (x+ x³ + x")1º (1 + x²)!' (x³ + x³ + x7). Justify your…

A: Given: px=x+x5+x7101+x211x3+x5+x7. To be find: the hundredth derivative of the given polynomial.…

Q: Consider the following functions. (x) = 2 + x, f,(x) = x, f;x) = x² g(x) = c,f,(x) + cof2(x) +…

A: A set of vectors {v1,v2,...,vk } is linearly independent if the vector equation x1v1+x2v2+···+xkvk…

Q: Use de Moivre’s theorem with n = 4 to prove that cos(4θ) = 8 cos^4 (θ) − 8 cos^2 (θ) + 1

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Q: Let f (x) = 5 In x бх Find the values of the coefficients in the expressions for f' (x) and f " (x)…

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Q: 3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b)…

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