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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the central difference formula for the first derivative?
💡 Hint: Think about how we approximate using points around x.
Question 2
Easy
What data points are needed for the second derivative approximation?
💡 Hint: Remember you need data from both sides.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the central difference formula use for its calculation?
- Only the point of interest
- Points on both sides
- Only previous points
💡 Hint: Think about the formula used for estimation.
Question 2
True or False: The central difference formula is less accurate than the forward difference formula.
- True
- False
💡 Hint: Consider how more data points influence accuracy.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the following data points: x = [1, 1.2, 1.4, 1.6, 1.8] and corresponding f(x) values = [0, 0.128, 0.544, 1.296, 2.432], apply the central difference method to estimate f′(1.6) and f′(1.4).
💡 Hint: Use the right data points and don’t forget the step-size in your calculations.
Question 2
Analyze the effect on the accuracy of the resulting derivative estimation if the spacing (h) between points is halved. Discuss how it relates to truncation and round-off errors.
💡 Hint: Consider both types of errors when adjusting h.
Challenge and get performance evaluation