We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Differential Equations : Definition of Laplace Transform

Study concepts, example questions & explanations for Differential Equations

Create An Account

All Differential Equations Resources

1 Diagnostic Test 29 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Definition Of Laplace Transform

Find the Laplace Transform for the following function.

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}$

Possible Answers:

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\frac{1}{s+5}, s>5$

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\frac{1}{s-5}, s>-5$

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\frac{1}{s+3}, s>-5$

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\frac{1}{s+5}, s>-5$

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\frac{1}{s+5}, s<-5$

Correct answer:

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\frac{1}{s+5}, s>-5$

Explanation:

To find the Laplace Transform for the following function

$\mathcal{L}\begin{Bmatrix} e^{-5t}\end{Bmatrix}$

use the transforms for basic functions which state,

$\mathcal{L}\begin{Bmatrix} 1 \end{Bmatrix}=\frac{1}{s}$

$\mathcal{L}\begin{Bmatrix} e^{at} \end{Bmatrix}=\frac{1}{s-a}$

$\mathcal{L}\begin{Bmatrix} e^{-5t} \end{Bmatrix}=\int_0^\infty e^{-st}e^{-5t}dt=\int_0^\infty e^{-(s+5)t} dt$

$\\=\frac{-e^{-(s+5)t}}{s+5}\bigg|_0^\infty \\\\=\frac{1}{s+5}, s>-5$

Report an Error

View Differential Equations Tutors

Shimelis
Certified Tutor

Alemaya Uniersity of Agriculture, Bachelor, Agricultural Engineering. Alemaya University, Master's/Graduate, Agricultural Eng...

View Differential Equations Tutors

Mary
Certified Tutor

Georgia Institute of Technology-Main Campus, Bachelor of Science, Applied Mathematics.

View Differential Equations Tutors

Sundeep
Certified Tutor

Indian Institute of Technology, Engineering in Computer Science, Electrical Engineering. New York University, Masters in Busi...

All Differential Equations Resources

1 Diagnostic Test 29 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Denver, SAT Tutors in Phoenix, GRE Tutors in Phoenix, MCAT Tutors in San Diego, LSAT Tutors in Boston, English Tutors in Miami, Physics Tutors in Phoenix, ACT Tutors in Phoenix, SSAT Tutors in New York City, SAT Tutors in Seattle

Popular Courses & Classes

LSAT Courses & Classes in Denver, SSAT Courses & Classes in Denver, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Los Angeles, GRE Courses & Classes in Chicago, GRE Courses & Classes in Miami, MCAT Courses & Classes in Miami, ACT Courses & Classes in Los Angeles, ACT Courses & Classes in New York City, ACT Courses & Classes in Seattle

Popular Test Prep

GRE Test Prep in Chicago, ACT Test Prep in Denver, MCAT Test Prep in New York City, LSAT Test Prep in Houston, ACT Test Prep in Boston, LSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Atlanta, ACT Test Prep in Los Angeles, ACT Test Prep in San Diego, LSAT Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Differential Equations : Definition of Laplace Transform

Study concepts, example questions & explanations for Differential Equations

All Differential Equations Resources

Example Questions

Example Question #1 : Definition Of Laplace Transform

All Differential Equations Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: