Question

at http://tutorial.math.lamar.edu/Classes/DE/LaplaceDefinition.aspx I don't understand the conditions in the answer of each example, can anyone please help me?

Answer 1

does it mean that the final answer should always be positive if yes then why?

Answer 2

You need to find solutions which are convergent. You don't want to end up with an answer of infinity so you place conditions on your c which will give you a function for your laplace transform rather than infinity.

Answer 3

a function in terms of your "c" or "s" or whatever else he's using. Take the first example: You're evaluating your integral in the interval (0,infin) ... it's an improper integral so you set it up as a limit the way the example shows. Now when you get to the last step you're presented with a limit as n--> infin of a certain expression. The limit of that expression will give you your function in terms of "c" but it will give you infinity if you don't place the c<0 condition while evaluating that limit.

Answer 4

it "could" give you infinity if you don't place the c<0 condition

Answer 5

@Leelee12 but why in first example c<0 in 2nd example s>0 it shows that all answers will definitely not be infinite but all of them will be positive too

Answer 6

OKKKKKKKKKKKKKKKKKKK got it

Answer 7

didn't read your second message as my screen was stuck now it's clear

Answer 8

thanks a tonne bro

Answer 9

sis* haha no problem