Practice Finite Difference Methods (3.2.1) - Numerical Differentiation and Integration

Practice: Finite Difference Methods

Lesson 3.2.1Numerical Differentiation and Integration

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9 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the formula for the forward difference method?
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Think about how it estimates the change at a point.
Question 2.
Explain what happens if h is too large in forward difference.
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Consider how large steps might affect accuracy.
3Question 3.
What is the main advantage of central difference over forward difference?
- Requires more data
- More accuracy
- Easier to compute
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Focus on the precision of the approximation.
4Question 4.
True or False: The backward difference is more accurate than the forward difference method.
- True
- False
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Consider the reliability of each method.
Question 5.
Given the function f(x) = x^3, use both forward and central difference methods with h = 0.1 to approximate f'(2). Compare the accuracy of your approximations.
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Use your calculated values of f for both methods to derive the results.
Question 6.
Analyze the performance of the backward difference method with various step sizes on f(x) = ln(x) around x = 1. What do you find?
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Evaluate each result and discuss.

5 more questions in this section. Enroll free to practise them all.