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## What are limits for Laplace transform?

If ϕ(s) is the Laplace tranfrom of f(t), then **lims→∞sϕ(s)=f(0+)**. and also lim→∞sϕ′(s)=limt→0+tf(t) since ϕ′(s) is the laplace transform of tf(t). These results suggest that lims→∞sϕ′(s)/ϕ(s) is finite, and indeed it is finite for many well-known Laplace tranforms.

## What are the conditions for existence of Laplace transform?

The function f(x) is said to have exponential order if there exist constants M, c, and n such that |f(x)| ≤ Mecx for all x ≥ n. **f(x)e−px dx converges** absolutely and the Laplace transform L[f(x)] exists. |f(x)| dx will always exist, so we automatically satisfy criterion (I).

## What is the purpose of Laplace transform?

The purpose of the Laplace Transform is **to transform ordinary differential equations (ODEs) into algebraic equations**, which makes it easier to solve ODEs.

## Can a Laplace transform be negative?

This is equivalent to the absolute convergence of the Laplace transform of the impulse response function in the region Re(s) ≥ 0. As a result, LTI systems are stable, provided that the poles of the Laplace transform of the impulse response function **have negative real part**.

## Is Laplace transformation nonlinear?

A single transform like Laplace, Sumudu, Elzaki etc can **not solve non linear problem**. To solve this types of problem need extension in these transforms.

## Which function Laplace transform does not exist?

Existence of Laplace Transforms. for every real number s. Hence, the **function f(t)=et2** does not have a Laplace transform.

## When can you use Laplace transform?

The Laplace transform is one of the most important tools used for solving ODEs and specifically, PDEs as it converts partial differentials to regular differentials as we have just seen. In general, the Laplace transform is used **for applications in the time-domain for t ≥ 0.**

## How is Laplace transform used in engineering?

Laplace Transform is widely used by **electronic engineers to solve quickly differential equations occurring in the analysis of electronic circuits**. 2. … Laplace Transform is used to simplify calculations in system modeling, where large number of differential equations are used.