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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does h represent in the context of finding a derivative using the central difference formula?
💡 Hint: Think about how we calculate the difference between points.
Question 2
Easy
Given f(2) = 4 and f(2.2) = 5, what is the approximate value of f'(2)?
💡 Hint: Use the central difference formula.
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 is the central difference formula used for?
- Estimating integrals
- Estimating derivatives
- Solving equations
💡 Hint: Recall its definition from our discussions.
Question 2
True or False: The step size (h) affects the accuracy of numerical differentiation.
- True
- False
💡 Hint: Think about the implications of our previous example.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a function given by the points x = [0, 1, 2, 3] and f(x) = [0, 1, 4, 9]. Use numerical differentiation to calculate the approximate value of f'(2). What do the results tell you about the behavior of the function?
💡 Hint: Consider the average slope between the points to determine the derivative at x = 2.
Question 2
Evaluate the error in your numerical differentiation for the given function values. If h = 0.5 and you find f'(2) using central difference, how would you verify the accuracy?
💡 Hint: Remember to analyze the difference between the calculated derivative and the true derivative.
Challenge and get performance evaluation