Practice Proof (for n=1) - 7.7 | 7. Multiplication by tn (Power of t) | Mathematics - iii (Differential Calculus) - Vol 1
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Proof (for n=1)

7.7 - Proof (for n=1)

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Laplace Transform of 1?

💡 Hint: Think of the integral from 0 to infinity.

Question 2 Easy

What is L{t}?

💡 Hint: Remember the basic derivatives.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the result of L{t * f(t)}?

F(s)
- (d/ds)F(s)
0

💡 Hint: Consider the relationship from the formula.

Question 2

The alternating sign in the multiplication property comes from:

True
False

💡 Hint: Think about differentiation rules.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

If L{f(t)} = sin(t), compute L{t * f(t)} and provide step-by-step justification.

💡 Hint: Follow through the differentiation carefully.

Challenge 2 Hard

For the function e^{-t} f(t) = e^{-t} * t^2, find the Laplace Transform and express using multiplication property.

💡 Hint: Carefully differentiate according to the rules.

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Reference links

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