The Dirac-delta function (δ(t - t0)) for t, t0 ∈ R, has the following property 

abϕ(t)δ(tt0)dt={ϕ(t0)a<t0<b 0otherwise

The Laplace transform of the Dirac-delta function δ(t - a) for a > 0; L(δ(ta))=F(s) is  

This question was previously asked in
GATE ME 2021 Official Paper: Shift 1
View all GATE ME Papers >
  1. eas
  2. e-as
  3. ∞ 
  4. 0

Answer (Detailed Solution Below)

Option 2 : e-as
Free
GATE ME 2023: Full Mock Test
5.7 K Users
65 Questions 100 Marks 180 Mins

Detailed Solution

Download Solution PDF

Explanation:

Dirac Delta Function

δ(ta)=limϵ0{0,<t<a1ϵ,ata+ϵ0,a+ϵ<t<ϵ

L[δ(t – a)] = e-as

0f(t)δ(ta)dt=f(a)

L[δ(ta)]=0estδ(ta)dt=eas

Latest GATE ME Updates

Last updated on Feb 19, 2024

-> GATE ME Answer Key has been released. The exam was held on 3rd, 4th, 10th, and 11th February 2024.

-> The Graduate Aptitude Test in Engineering, also known as GATE, conducts an Entrance exam that serves as a gateway for all Engineering aspirants.

->  Candidates who want a successful selection can refer to the GATE ME Preparation Tips to boost their exam preparation and increase their chances of selection.

->  Candidates must attempt the GATE ME Mock tests

Get Free Access Now
Hot Links: teen patti joy mod apk teen patti real cash apk teen patti master gold teen patti bodhi