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Q5 a) b) (x > 0,k > 0) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of the function f(x) = 2x, (-1

Q5 a) b) (x > 0,k > 0) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of the function f(x) = 2x, (-1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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Solve Q5
Q2 a) Using Laplace transformation, solve the equation Q3 Q4 Q5 y + y = r(t), r(t) = tif 1 < t < 2 and 0 otherwise. y(0) = 0, Y(0) = 0 b) Show that the form under the integral sign is exact in the plane and evaluate the integral (2,4,0) ex-y+z² (dx-dy + 2zdz) (0,-1,1) a) Find the directional derivative of the function f = In (x² + y²) at the point P(4,5) in the direction of the vector a = î -Ĵ b) Using Convolution, calculate the value of L-1¹ [2(5²+1 a) Using Gamma function evaluate x6e-3x dx. Find the Fourier Transformation of f(x) = b) Sxe-x, x > 0 0, x < 0 xe a) b) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of the function f(x) = (x > 0, k > 0) 2x, (-1<x< 1) with period 2.
Transcribed Image Text:Q2 a) Using Laplace transformation, solve the equation Q3 Q4 Q5 y + y = r(t), r(t) = tif 1 < t < 2 and 0 otherwise. y(0) = 0, Y(0) = 0 b) Show that the form under the integral sign is exact in the plane and evaluate the integral (2,4,0) ex-y+z² (dx-dy + 2zdz) (0,-1,1) a) Find the directional derivative of the function f = In (x² + y²) at the point P(4,5) in the direction of the vector a = î -Ĵ b) Using Convolution, calculate the value of L-1¹ [2(5²+1 a) Using Gamma function evaluate x6e-3x dx. Find the Fourier Transformation of f(x) = b) Sxe-x, x > 0 0, x < 0 xe a) b) Find the Fourier cosine integral of f(x) = e-kx Find the Fourier series of the function f(x) = (x > 0, k > 0) 2x, (-1<x< 1) with period 2.
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