Practice Definition (1.1.1) - Finite Differences - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is a finite difference?
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Think about how derivatives relate to changes in functions.
Question 2.
How do you express a forward difference mathematically?
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What happens when we increase x by a small step h?
3Question 3.
What does a finite difference represent?
- The exact value of a function
- The change in function value
- The graphical representation of a function
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Consider what happens when inputs vary slightly.
4Question 4.
Is the formula for a backward difference ∇f(x) = f(x) - f(x - h)?
- True
- False
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Look at how we evaluate past function values.
Question 5.
Given f(x) = sin(x), find the first and second forward differences at x = π/4 with a small increment h = 0.1.
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Use calculator or table values to evaluate sin at the required points.
Question 6.
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.
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Follow the systematic method for creating a difference table.

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