a) Find the Laplace transformation of the function f(t) = cosh at sinh bt
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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Question
Solve Q a
![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)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff297114c-ed17-40e3-bb40-78b98ac3f9da%2F84ecc700-11c8-4602-bcb6-b6c0624f0a18%2F63385ii_processed.jpeg&w=3840&q=75)
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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