Practice Proof of Second Derivative - 1.1.6 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
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Proof of Second Derivative

1.1.6 - Proof of Second Derivative

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the formula for the Laplace Transform of the first derivative?

💡 Hint: Recall how derivatives are transformed.

Question 2 Easy

Write down the definition of exponential order.

💡 Hint: Think about how functions behave at infinity.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Laplace Transform of the first derivative give you?

s^2F(s) - f(0)
sF(s) - f(0)
F(s) - f(0)

💡 Hint: Think back to the formulaapplied to f(t) and it's derivative.

Question 2

True or False: The Laplace Transform can be used for higher-order derivatives.

True
False

💡 Hint: Recall the generalization discussed for n-th derivatives.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the function f(t) = e^{2t}, compute L{f''(t)} and verify the initial conditions.

💡 Hint: Apply the basic rules of Laplace for differentiating functions.

Challenge 2 Hard

Create and solve an initial value problem for a second-order linear ODE using the Laplace Transform.

💡 Hint: Use the formula for L{y''(t)} in your setup.

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