Consider the function f(x) = x = [0,2]. Construct the , Lagrange interpolation polynomial which interpolates the function f(x) at x = 0, x₁ = 1 and ₂ = 2.

Q: a. The total cost of 11 pencils and 3 erasers is $64 and the total cost of 8 pencils and 3 erasers…

A: Given that  The total cost of 11 pencils and 3 erasers is $64 The total cost of 8 pencils and 3…

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Q: Q3:what is the difference between the finite element and finite volume method

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Q: Use Simpson's 1/3rd rule to find -0.6 dx by taking seven ordinates. (nr

A: Here, we need to use simpson's 1/3rd rule and need to take seven ordinates. so h=0.1

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Q: Use energy method to show that the following PDE p(x)un - [k(x)uz q(a)u, 0 0, u(0, x) = u(0,r) = 0,…

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Q: Solve differential equations 1. y - xy = 0; M(1,1). - 2. y4y² = 1; M(1,0). 3. y 4. yy ry³ = 0;…

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Q: dx Example 8.10. Evaluate So by using (i) Trapezoidal rule, 2 1 + x² (ii) Simpson's 1/3 rule, (iii)…

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

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Q: 1 8) Find the Laurent series of f(z) = (2-1)(z-2) if 1 < |z| <2

A: Here we have to find laurent series of f(z) in given interval

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Q: 8) Find the Laurent series of f(z) = TO NIH + + b) c) d) NOTA + + №w + + 1 (2-1)(z-2) I 79 if 1 <…

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Q: 28-3 3. £*{F(s)} for F(s)=3² +5-2

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Q: 5: Let R=(Z,+, .). Find Chan Idempotent element of R e) Is R a field? Why? c) Nilpotent elements of…

A: We have to find the nilpotent and idempotentent element of R.

Q: 4. Show that a sublinear functional p satisfies p(0) = 0 and p(-x) ≥-p(x).

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Q: Given the system of linear equations, X + Y 2, X + 2y + Z 3, X + Y + (k²-5)z k, where k is a…

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Q: 2. x=9-y², y-axis; about x = 9

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Q: 3. Find the maximum and minimum values of z-a 1-āz on 2 ≤ 1 (where a with la| < 1 is fixed)

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Q: Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the…

A: As per guidelines we can do only 3-subparts.

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: Find the following. u = v =   a) || u || b) || v || c) || u+v || d) || u/ ||u|| || e) || v /…

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Q: 8) For each case, determine the form of the Porticular Solution (DO NOT SOLVE) a) y" - 4y +134= e…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: (d) A commutative ring R is a prime ideal of itself. (e) If p and q are primes, then there is a…

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Q: QUESTION 1. Find the Laplace transform of the following functions. Here, represents con volution. a)…

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Q: Using (a) Jacobi Iterative Method and (b) Gauss-Seidel Method, obtain the solution [12x₂ + 3x₂ −5x₂…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: (a) Let a, b, c E R³. If det (a, b, c) 0, prove that a, b and c are non-zero. (b) Prove that x x…

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

Q: 3. Determine if b is a linear combination of a₁, a2, and a3. 2 3 a1 = 1 , A2 = 2 , az = 1 b= 4 1 1 0…

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Q: 1. Prove that the following functions are quasi-concave: (i) f(x, y) = xy¹, x > 0, y> 0; (ii)…

A: Given: fx,y To find: Quasi-concave function

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Q: 9) If f(z)=u- iv is analytic in the z-plane, then the C-R equations satisfied by it's real and…

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Q: Example 9.6. The integers 0, 1, 1, 2, 3, 5, 8, 13, 21, are said to form a Fibonacci sequence. Form…

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Q: Example 9.2. From y = A2" + B(-3), derive a difference equation by eliminating the constants.

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Q: 7.) Solve а) y'+y'-by=0 6-) у"-ну' +13y=0 с.) у" -бу' +ац=0

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Q: Find the Laurent series of f(z) = (2-1)(z-2) if 1</z] <2

A: Here we have to find laurent series of f(z) in given interval