Question: Show that the function f(t) = 1/t 2 does not possess a Laplace transform. Write {1/t 2 } as two improper integrals: Show that I

Show that the function f(t) = 1/t2 does not possess a Laplace transform.

Write ℒ{1/t2} as two improper integrals:

st L{1/r²} dt+ -dt 1 + 1. %3D


Show that I1 diverges.

st L{1/r} dt+ -dt 1 + 1. %3D

Step by Step Solution

★★★★★

3.34 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that the function f t 1t 2 does not possess a La... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related A First Course in Differential Equations Questions!

Q:

Show that the function f (t) = 1/t 2 has no laplace transform. for this, write L [1/t 2 ] as the sum of two improper integrals, then show that at least one of the integrals diverges {1/P} = e-st -dt+...

Q:

Show that the function f defined by f (x) := x = x/x2 + 1; x R, is a bijection of R onto {y : 1

Q:

Show that the function f (x) in Example 3-5 satisfies the properties of a probability mass function by summing the infinite series.

Q:

Math 1152 Project #4 Solving Initial Value Problems using Power Series and the Laplace Transform Due: Tuesday, April 11 Name(s): - - - - - - - - - - - - - - - - - - - - Description - - - - - - - - -...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Q:

3. So far, we have always assumed that there is no latent heat to account for. For a simple example, we can formulate a model with latent heat effects and solve it using a similarity solution....

Q:

Consider the function f ( x) = tan -1( tan x ). Then f (0) =f (x) =0. Your professor claims that by the Mean Value Theorem, there is a number con (0, x) such that f(c) =0. (a) Prove your professor...

Q:

Solution Suppose f x f x Note that if x is odd and x is even then we will have x 1 x 1 i e x x 2 which is impossible Similarly the possibility of x being even and x being odd can also be ruled out...

Q:

Conservative Company purchased a warehouse on January 1, 2011, for $400,000. At the time of purchase, Conservative anticipated that the warehouse would be used to facilitate the expansion of its...

Q:

A 20 kg block on a horizontal surface is attached to a horizontal spring of spring const ant k = 4.0kN/m. The block is pulled to the right so that the spring is stretched 10 cm beyond its relaxed...

Q:

Treasury bonds are registered at the New York Stock Exchange, but the secondary market trading occurs over - the - counter. a . True b . False

Q:

What other processes may be improved with driverless cars?

Q:

Divide the data set into age groups (above/below the median), and use nonparametric methods to test whether the number of days abstinent from smoking is related to age?

Q:

Use the same approach as in Problem 9.27 to test whether the amount previously smoked is related to the number of days abstinent from smoking?

Q:

Use the same approach as in Problem 9.27 to test whether the adjusted carbon monoxide (CO) level is related to the number of days abstinent from smoking?

Q:

What will a deposit of $4.500 left in the bank be worth under the following conditions. Left for nine years at 7% interest Left for six years at 10% compounded semiannually Left for five years at 8%...

Q:

What can we infer from the fact that the correlation coefficient between Project Jimmy and Project Walter was equal to -1.00? That there will be no diversification gain between the two projects That...

Q:

[10 points] You have a loan outstanding. It requires making ten payments of $10,000 each, with the first payment due today and the remaining nine payments at the end of the next 9 years. Your bank...