Find an orthonormal basis of the plane ¤1 + 5x2 – x3 = 0. %3D

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Q: Exhibit infinitely many prime elements in each of the following two rings: (i) R[x]. (ii) Z3[x].

A: Solution :-

Q: 3. Find the volume V of the solid whose base is an elliptical region with boundary curve 16x² + 25y?…

A: Area of triangle=(1/2)(base)*(height) Area of semicircle=(1/2)π(radius)^2

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Q: B: Solve the following P.D.E a2u + 2, u(0,y) = 0 , ux (x,0) = x² , Use the general method. a x ди…

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Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}c S,

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A: We have used the iteration formula of Newton's method.

Q: Problem 5. Let B = {T1, 72} be an ordered basis for R? , and y = for R? {71, 72} be another ordered…

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Q: 1. Let f : R? → R be a function with continuous partial derivatives at least up to the second order.…

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Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

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Q: Find the average value of the function f(x,y)=x+ey over the rectangular region R=[0,2]×[0,2].

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Q: Write the multiplication table for the following commutative quotient ring: Z2[x]/(x³ + x² +x + 1).

A: Solution: The multiplication table below:

Q: 4. Evaluate the integral 9 f(z) dz, where C is the unit circle centered at the origin D=64 sin(D*z)…

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Q: consider the equation solution of the differential equation is of the form y" + ay' + by = f(x),…

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Q: Evaluate determinant D by:

A: Here we have to solve the determinant of given matrix using Chios method.

Q: sin (4t) + 2c

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. = 13, x, = (1, 2,…

A: Note: Let A be a square matrix and x be an eigen value of A. A non-zero vector V is said to the…

Q: Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n > 3, an = 2an-1+ bn-1 for n > 2 bn = bn-1+ ɑn-1 express…

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Q: (1) Show that the series n+1 n-1 and n3 +1 n3 – 1 n=2 converge. Be very clear about the steps you…

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Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Problem 3. Recall that a = ebina for all a >0 and all b. (1) Compute the limit lim (1+ )" by…

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Q: Consider the equation y" + ay' + by=f(x) where a and b are real constants. If the general solution…

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Q: (푸+이)- (+0) + . 13. Answer the questions by comparing the equation, f(x) = 7 cos (x+ 9 +1, to the…

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A: We have  Px,y=9x2+36xy-4y2−18x−18ygx,y=3x+4y-32 The Lagrangian is: Lx,y,λ=Px,y+λgx,y So,…

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Q: Problem 22.8 Solve by Laplace transform Utt - 9urr = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u (x,0) = 0,…

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Q: (a) Find all cosets of the subgroup 4Z of Z. (b) Find all cosets of the subgroup (4) of Z,2. (c)…

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Q: Find the derivative of the function at Poin the direction of A g(x, y) = x – (y²/x) + V3 sec (2ry),…

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Q: A thermometer reading 60° F is placed in an oven preheated to a constant temperature. Through a…

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