Practice Numerical Differentiation (3.2) - Numerical Differentiation and Integration

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6 sample questions

Question 1.
What is numerical differentiation?
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Think about derivatives and how they're calculated.
Question 2.
Describe the forward difference method.
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Recall the formula for forward difference.
3Question 3.
What is numerical differentiation?
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Remember, it relates to how we deal with derivatives.
4Question 4.
The error for central difference method is proportional to which order?
- True
- False
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Consider how that compares to forward and backward differences.
Question 5.
Using the function f(x) = x^3, calculate the derivative at x=2 using both the forward and central difference methods with h = 0.1. Compare your results and discuss accuracy.
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Remember to apply the formulas for both methods correctly.
Question 6.
Discuss the implications of selecting different values for h in numerical differentiation in a real-world context, such as robotics or physics simulations.
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Consider the trade-offs seen in actual applications.

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