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Laplace Transforms and Step Functions

Laplace Transforms and Step Functions

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Patricia Brown

FREE Resource

The video tutorial explains how to find the Laplace transform of a piecewise function using unit step functions. It begins with an introduction to the concept and proceeds to rewrite the function in terms of step functions. The function is then simplified using the distributive law, and the Laplace transform is applied to the simplified function. The tutorial concludes with the final steps of the Laplace transform process, highlighting key rules and simplifications.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is one method to find the Laplace transform of a piecewise function?

Utilizing Taylor series

Applying unit step functions

Employing integration by parts

Using Fourier series

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the activation of a piece in a step function represented?

By adding a constant

By subtracting a constant

By using a unit step function

By multiplying by zero

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to terms multiplied by zero in the simplification process?

They become one

They double in value

They remain unchanged

They are eliminated

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to terms with the same coefficient but opposite signs in the simplification?

They are subtracted

They cancel each other out

They are added

They are multiplied

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the Laplace transform of a unit step function U(t-a)?

s times the Laplace transform of the function

1/s times the Laplace transform of the function

e^(as) times the Laplace transform of the function

e^(-as) times the Laplace transform of the function

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of the Laplace transform of T?

s

1/s^2

s^2

1/s

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you handle the Laplace transform of a constant function?

It is one

It is 1/s

It is s

It is zero

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