Practice Finite Differences (1.1) - Finite Differences - Mathematics - iii (Differential Calculus)

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9 questions

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6 sample questions

Question 1.
What is the formula for the forward difference?
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Think about how the function values change with a small increment.
Question 2.
What is the backward difference at point x?
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Consider the value at the current point and the previous point.
3Question 3.
What does the forward difference measure?
- Decrease in function value
- Change in function value as x increases
- Average change
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Recall the forward difference formula.
4Question 4.
True or False: The central difference provides less accuracy than the forward and backward differences.
- True
- False
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Consider the definitions of each type of difference.
Question 5.
Given the function f(x) = sin(x) at x = 0, π/6, π/3, π/2, find the first forward differences.
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Substitute the values of sin function at the mentioned points.
Question 6.
Derive the central difference formula from the definitions of forward and backward differences.
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Consider the symmetrical nature of central differences.

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