Use Theorem 7.4.1.
THEOREM 7.4.1 Derivatives of
Transforms
If
F(s) = ℒ{f(t)}
and
n = 1, 2, 3, . . . ,
thenℒ{tnf(t)} = (−1)n
dn |
dsn |
F(s).
Evaluate the given Laplace transform. (Write your answer as a function of s.)
ℒ{t cos(7t)}
Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = ℒ{f(t)} and n = 1, 2,...
Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = ℒ{f(t)} and n = 1, 2, 3, . . ., then ℒ{tnf(t)} = (−1)n dn dsn F(s). Evaluate the given Laplace transform. (Write your answer as a function of s.) ℒ{3t2 cos(t)}
Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, ..., then L{"f(t)} = (-1)". F(s). Evaluate the given Laplace transform. (Write your answer as a function of s.) L{t cos(7t)} Find the general solution of the given differential equation. +3y= -* YOU) - Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) Determine whether there...
L{t"f(t)} = (-114 d Fis). Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, .., then ds" Evaluate the given Laplace transform. (Write your answer as a function of s.) L{t cos(50)}
Use Theorem 7.4.1.THEOREM 7.4 .1 Derivatives of TransformsIf F(s)=L{f(t))} and n=1,2,3, ……, then
Use Definition 7.1.1,DEFINITION 7.1.1 Laplace TransformLet f be a function defined for t ≥ 0. Then the integralℒ{f(t)} = ∞e−stf(t) dt0is said to be the Laplace transform of f, provided that the integral converges.to find ℒ{f(t)}. (Write your answer as a function of s.)f(t) = cos(t),0 ≤ t 0)
Use Theorem 7.1.1 to find ℒ{f(t)}. (Write your answer as a function of s.)f(t) = t2 + 4t − 2ℒ{f(t)} =
Use Theorem 7.1.1 to find ℒ{f(t)}. (Write your answer as a function of s.)f(t) = 10t − 8ℒ{f(t)} =
Use Definition 7.1.1.DEFINITION 7.1.1 Laplace TransformLet f be a function defined for t ≥ 0. Then the integralℒ{f(t)} = ∞e−stf(t) dt0is said to be the Laplace transform of f, provided that the integral converges.Find ℒ{f(t)}. (Write your answer as a function of s.)f(t) = et + 2ℒ{f(t)} = (s > 1)
Use Definition 7.1.1.DEFINITION 7.1.1 Laplace TransformLet f be a function defined for t ≥ 0. Then the integralℒ{f(t)} = ∞e−stf(t) dt0is said to be the Laplace transform of f, provided that the integral converges.Find ℒ{f(t)}. (Write your answer as a function of s.)f(t) = 9, 0 ≤ t
(1 point) Use the "Integration of Laplace Transforms Theorem" to find the Laplace transform of the function sin(f) f(t) 7t Lif() 7*In(u^2+1)