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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a finite difference?
💡 Hint: Think about how derivatives relate to changes in functions.
Question 2
Easy
How do you express a forward difference mathematically?
💡 Hint: What happens when we increase x by a small step h?
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 a finite difference represent?
- The exact value of a function
- The change in function value
- The graphical representation of a function
💡 Hint: Consider what happens when inputs vary slightly.
Question 2
Is the formula for a backward difference ∇f(x) = f(x) - f(x - h)?
- True
- False
💡 Hint: Look at how we evaluate past function values.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given f(x) = sin(x), find the first and second forward differences at x = π/4 with a small increment h = 0.1.
💡 Hint: Use calculator or table values to evaluate sin at the required points.
Question 2
Suppose you have the data values f(x) at x = 1, 2, 3, 4. Show how these can be used to create a difference table to find approximations for higher order derivatives.
💡 Hint: Follow the systematic method for creating a difference table.
Challenge and get performance evaluation