1.1.1 - Definition
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Practice Questions
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What is a finite difference?
💡 Hint: Think about how derivatives relate to changes in functions.
How do you express a forward difference mathematically?
💡 Hint: What happens when we increase x by a small step h?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does a finite difference represent?
💡 Hint: Consider what happens when inputs vary slightly.
Is the formula for a backward difference ∇f(x) = f(x) - f(x - h)?
💡 Hint: Look at how we evaluate past function values.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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