3.6 - Summary of Key Concepts
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Practice Questions
Test your understanding with targeted questions
What does the forward difference formula approximate?
💡 Hint: Think about how we use previous and future values to estimate a rate of change.
Which integration method uses polynomial interpolation?
💡 Hint: These formulas fit a polynomial to discrete data points.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the central difference method’s error reduction rate?
💡 Hint: Use 'h' to think about how error varies.
True or False: The trapezoidal rule provides a higher accuracy than Simpson's rule.
💡 Hint: Remember which method fits a line and which fits a curve.
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Challenge Problems
Push your limits with advanced challenges
Using a data set of (1, 3), (2, 5), and (3, 9), compute the derivative at x=2 using the forward and backward difference methods. Compare their results.
💡 Hint: Calculate both approximations and discuss why they differ.
If given the integral of sin(x) from 0 to π using Simpson’s Rule with n=2 intervals, calculate and compare it to the value obtained through trapezoidal rule.
💡 Hint: Assess how both methods depict the shape and area under the curve.
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