2. Consider periodic function [0, -

Q: Let f(x) be periodic with period 2pi and defined on [0, 2pi] as follows:f(x) = 1 if 0 ≤ x ≤ pi/2f(x)…

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Q: 5. Residue theorem Use the residue theorem to compute (a) ro∞ t2+1 dt.

A: Given integral is∫0∞t2+1t4+1dtThe integral is computed using Residue theorem as shown below.

Q: 1 (-0 + 7) - 1 Sketch a graph of the function f(0) = -3 sin(-0+

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Q: Find Lim (x² (X, Y) → (0, 0) + Y²) Log (x² + Y²)

A: To find the limit  lim(x,y)→(0,0)(x2+y2)log(x2+y2)

Q: The Fourier transform of a function } (t) iš defihed by F(w) = f(t)e-jwtdt %3D a) Using the above…

A: The Fourier transform of a function f(t) is defined by F(ω)=∫-∞∞f(t) e-jωt dt 1) We have to find the…

Q: If a, b = R be fixed positive numbers such that for all x f(a + x)=b+ [b³ + 1-3b². f(x) + 3b{f(x)}²…

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Q: f(t) = 8 + 6t+2t², for- n<t<π, Show Transcribed Text and extend to a 2π periodic function.

A: The given function is ft=8+6t+2t2  for -π&lt;t≤π. To extend the function to a 2π periodic function.…

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

Q: lim, ol cos(a)x – cos (b)x

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Q: Define a harmonic function. (b)Prove whether u(x, y) = x² - 2xy + y² is a harmonic function on a set…

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Q: Q: If f (x) is a polynomial function of the nth degree prove that fe'f(x) dx =e* {f(x)-f (x)+ f…

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Q: Let f(x) be a function f:[−1,1]→[0,1], f(x)=x^2. Let g(x):(−∞,∞)→[0,1] be a function such that g(x)…

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Q: A function f satisfies the condition f(x+T)= -f(x) for all . Show that all its even Fourier…

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Q: .  (a) Sketch the graph of y = 2x2 over the interval [-1,1] (b) Let x be any point in the interval…

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Q: A periodic function f(x) = g(x+2x) f (x +27) us given by x+ π -TULX LO π-x, 0≤xs t 2 a) Sketch f(x)…

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Q: Consider the function f(x) = cos(2x) for -2pi &lt; x ≤ 2pi and zero otherwise.A) Show that it meets…

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Q: 5. Find limx→∞ f (X), if it exists. (a) f(x) = log(x² + 2y² + 4z²) x² + y² +2² (c) f(x) = e(x+y)²…

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Q: 2) Find the complex Founer senes of a 2c - periodic function f, which is defined as f(x)= (ix-1)² in…

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Q: Find lim n→∞ n + cos(x) Jo ne + sin(x) So -dr.

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: erfind the first agd decond derivatives oh the funchan

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Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

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Q: y), the harmonic conjugate of u. Form the

A: A function u (x, y) is said to be a harmonic function if u _x x + u_ y y = 0.

Q: The function (f) with a period of 2π is defined by: f(x) = cosh (x - 2π)  if x∈[π ; 3π] a)…

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Q: skla 8. What is the value of Fourier discrete function & [k] at k = 1?

A: To determine: The value of the Fourier discrete function δk at k=1.

Q: Classify the zeroes (according to order) and isolated singularities of (2² - 1)e¹/² cos (TZ) (z + 2)…

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