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a) Find the Laplace transformation of the function f(t) = cosh at sinh bt

a) Find the Laplace transformation of the function f(t) = cosh at sinh bt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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a) Find the Laplace transformation of the function f(t) = cosh at sinh bt b) Find v2f 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 a= 2î - 4j e) f) State Green's theorem in plane. 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) (1; 0 < t < 1 i) Find L[f(t)], Where f(t) = 2; 2 <t<4 (0; t> 4 j) 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 v2f 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 a= 2î - 4j e) f) State Green's theorem in plane. 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) (1; 0 < t < 1 i) Find L[f(t)], Where f(t) = 2; 2 <t<4 (0; t> 4 j) Find the value of L-¹ s²+6 [(s²+1)(s+4)]
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