Find the Fourier series (ao, an, bn and the fourier series formula) f(x) = {0 if − 2 < x < −1 f(x) = {6 if − 1 < x < 1 f(x) = {0 if 1 < x < 2

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Q: 2 Express (+) in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] O 3 [cos 70+isin 70] O 13…

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Q: Q2\ Evaluate : fot√x dx

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Q: (8) If F is a field, then it has no proper ideal. От F

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Q: ind Laplace Transform of the expression. f(t) = e-5 H (t-2)

A: Sol Le-tHt-2 Apply transform rule:  if Lft=Fs then  Leatft=Fs-a

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Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2).

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Q: Solving the following problem using Fourier transformation method. du d²u = 0, (t>0,-∞0< x <∞0) Ət…

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Q: (5) In commutative ring with identity each proper ideal is contained in prime ideal. От F

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Q: Problem 3: Use secant method to estimate a root for function f(x)= x³ -0.6x² -3.5x+ 3.5-0, starting…

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Q: a. Solve the initial value problem (x² - 1)y" + 4xy' + 2y = = y (0) = -1, given that 1 1 Y1 and Y2…

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Q: with 5 and 8 the Di

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Q: Let X be co or lº, 1 ≤ p ≤ ∞o. Consider the operator Prove that U is not compact but U² is compact.…

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Q: Q2. Solve the following differential equation by variation of parameters: d²y x3 dx² +6x³. dy dx -3x…

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Q: d) Give a formula for the coefficient of ak in the expansion of where k E Z. 100

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Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

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Q: 20.22. (a) Suppose that X₁ ≤X₂ ≤. ... and that Xp X. Show that X, →X with n probability 1. (b) Show…

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Q: . Use the Ratio Test to determine if the following series converges or diverges. n! Σn=1 (2n+1)!

A: Given series is ∑n=1∞n!(2n+1)!   Let  un=n!(2n+1)!

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2). (b)…

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Q: (7) The set H={0,1,2}is a subring of (Z4, +4,.4) integer ring module 4. T OF

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Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

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Q: Q1: Find the general solution for the following first order D.Es? (Answer two only) a) sinx+cosh…

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Q: 3. Find the solution of the following system of liner inequalities by graphing- (K + 2y > 5x + 3y…

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Q: Q2) Find and sketch the trigonometric Fourier series corresponding to the saw tooth signal as shown…

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Q: (e) A student writes down the following piece of work, which contains an error in the reasoning. The…

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Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…