Practice Proof Of Second Derivative (1.1.6) - Laplace Transform of Derivatives

Practise this section

8 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the formula for the Laplace Transform of the first derivative?
Show hintHide hint
Recall how derivatives are transformed.
Question 2.
Write down the definition of exponential order.
Show hintHide hint
Think about how functions behave at infinity.
3Question 3.
What does the Laplace Transform of the first derivative give you?
- s^2F(s) - f(0)
- sF(s) - f(0)
- F(s) - f(0)
Show hintHide hint
Think back to the formulaapplied to f(t) and it's derivative.
4Question 4.
True or False: The Laplace Transform can be used for higher-order derivatives.
- True
- False
Show hintHide hint
Recall the generalization discussed for n-th derivatives.
Question 5.
Given the function f(t) = e^{2t}, compute L{f''(t)} and verify the initial conditions.
Show hintHide hint
Apply the basic rules of Laplace for differentiating functions.
Question 6.
Create and solve an initial value problem for a second-order linear ODE using the Laplace Transform.
Show hintHide hint
Use the formula for L{y''(t)} in your setup.

4 more questions in this section. Enroll free to practise them all.