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(1; 0 < t < 1 i) Find L[f(t)], Where f(t) = 2; 2 < t < 4 0; t>4

(1; 0 < t < 1 i) Find L[f(t)], Where f(t) = 2; 2 < t < 4 0; t>4

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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a) Find the Laplace transformation of the function f(t) = cosh at sinh bt b) Find 2f where f = e2x sin2y. c) Write the sufficient condition for existence of Laplace transformation of a function. d) Find the Directional derivative of the function f = x² + y² at a point p (1,1) in the direction ä2î - 4j e) State Green's theorem in plane. f) Find the Laplace transformation of the unit impulse function 8(t-22017) and The unit step function U(t-22017) g) Find the Fourier sine series of the function f(x)=-100¹0(-n < x <n); f(x)= 100¹0(0<x<n) h) Find a parametric representation of the Parabolic equation z = 9(x² + y²) i) j) (1; 0 < t < 1 Find L[f(t)]. Where f(t) = 2; 2 <t<4 (0; t> 4 Find the value of L-1 s² +6 [(s²+1)(s+4)]
Transcribed Image Text:a) Find the Laplace transformation of the function f(t) = cosh at sinh bt b) Find 2f where f = e2x sin2y. c) Write the sufficient condition for existence of Laplace transformation of a function. d) Find the Directional derivative of the function f = x² + y² at a point p (1,1) in the direction ä2î - 4j e) State Green's theorem in plane. f) Find the Laplace transformation of the unit impulse function 8(t-22017) and The unit step function U(t-22017) g) Find the Fourier sine series of the function f(x)=-100¹0(-n < x <n); f(x)= 100¹0(0<x<n) h) Find a parametric representation of the Parabolic equation z = 9(x² + y²) i) j) (1; 0 < t < 1 Find L[f(t)]. Where f(t) = 2; 2 <t<4 (0; t> 4 Find the value of L-1 s² +6 [(s²+1)(s+4)]
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