2x d³y d'y dx³ dx² 2 = d²y_a². dx2

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Q: 4. a) Prove that I A i) V=I- I+A 1+A ii) fx+nh = Σx=0 (1) 4k fx. =

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Q: а) Рrоⅴе thаt І = { f(х) ∈ ℤ[х] : f(0) іѕ еⅴеո } іѕ аո іⅾеаⅼ оf ℤ[х].

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Q: Derive Σ PIN) = 1 from equation 1 1. N=O eq] P(N) = N'`~ N! Hint Sex ≤ x² n₂D nl [nd e N

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Q: n²(x-1)" Find the radius of convergence, R. for the power series Σ(-1)"? 2-n! OR=1 OR=2 OR=0 OR=∞

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Q: Consider the function f(t) = 9 sec² (t) - 3t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: d. Let t = H hours be the time during the workday (0 ≤ t ≤8) when G(t) = 100. N(t) = 20(t -…

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Q: When the Simpson's rule is used to 2 S²x 0 approximate the integral absolute error is 2.6667 1.6667…

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Q: Q1/ Solve the equation: 4fxx(x,t)=ft(x,t) f(x, 0)=20(6-x) f(0,t)=0 f(6,t)=0 Take h=1 for 0< t <2 and…

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Q: 4. a) Prove that A i) V=I I+A 1+A ¡¡) fx+nh = Σx=0 (7) 4¹ fx.

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Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

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Q: (a) (i) (ii) In the diagram below, M, L and K are points on the surface of the earth. (n-3.142 and…

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Q: Find and sketch the domain of f(x, y) = √√₁ - (x + 1)² − y² + 2ln(x − y + 1)

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