Question

How do I use the table of transforms, linearity, and s-shifting (if necessary) to find f(t) = L^−1 (F(s)) for these?

F(s) = (1/(s + 1) + (3/ s^2 + 4))

F(s) = ((s + 3)/(s^2 + 3s + 2))

For the second one I was given a hint to find the partial fraction decomposition first.

Answer #1

I have a few questions that I'm not sure how to go about doing?
This is what I was asked:
Use the table of transforms, linearity, and s-shifting to find
F(s) = L (f(t)) for each of the following functions. Write the
result as a rational function P(s)/Q(s).
1) f(t) = −4 + e^(−t)
2) f(t) = e^(4t) − 10 + sin t
3) f(t) = cos(2t − 5) (Hint: use the identity cos x ± y = cos x...

Use partial fraction decomposition to find the inverse Laplace
transform of the given function.
(a) Y (s) = 2 /(s 2+3s−4)
(b) Y (s) = 1−2s /(s 2+4s+5)
differential eq

Use Laplace transforms to find the solution of ?′′(?) + 2?′(?) +
2?(?) = 2 with ?(0) = 0 and ?′(0) = 0
First, find an equation for ?(?), the Laplace transform of ?(?)
Second, simplify ?(?) using partial fractions if necessary Third,
find the inverse transform of ?(?)

1. Find the Laplace transform of
a.) f(t)=u(t−4)⋅e^t
F(s)=
2. Find the inverse Laplace transform of
a.) F(s)=2e^(−3s)−e^(−2s)−3e^(−6s)−e^(−9s)/s
f(t) =
b.) F(s)=e^(−6s)/s^2−3s−10
f(t) =
c.) F(s)=4e^(−9s)/s^2+16
f(t) =

Given the following functions F(s), find f(t). Do not enter u(t)
as part of your answers, and do not use any truncated decimal
approximations to fractions or they will be marked wrong (answers
must be exact). E.g., enter (2/3), not 0.666.
(a) F(s) = s + 7 /(s(s + 3)(s + 8))
(b) F(s) = (s^2 + s + 6)/( s(s + 1)(s + 8))

1. Find the partial fraction decomposition of the rational
function:
(2s − 4)/(s^2 + s)(s^2 + 1)
2. Find:
∫ (9x)/(sqrt. root(25-x^2)) dx + ∫ (3)/(sqrt.
root(25-x^2)) dx (use C for constant of integration).
3. Evaluate the following integral:
∫ 17t sin^2(t) dt

1. f(x, y, z) = 2x-1 − 3xyz2 + 2z/
x4
2. f(s, t) = e-bst − a ln(s/t) {NOTE: it is
-bst2 }
Find the first and second order partial derivatives for question
1 and 2.
3. Let z = 4exy − 4/y and x =
2t3 , y = 8/t
Find dz/dt using the chain rule for question 3.

let f(0)=1, f'(0)=-1, F(s) = L{f(t)}(s), F''(s) = -9s/(s^2+9).
find f(t)

Chapter 13, Problem 13.26 (Circuit Solution)
Given the following functions F(s),
find f(t). Do not enter u(t) as
part of your answers, and do not use any truncated decimal
approximations to fractions or they will be marked wrong (answers
must be exact). E.g., enter (2/3), not 0.666.
(a) F(s)
=
s + 6
s(s + 4)(s + 10)
(b) F(s)
=
s2 + s + 3
s(s + 5)(s + 6)

how
do i know when to use z table t table x^2 table?

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