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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Q3
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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