Practice Python Code Example (trapezoidal Rule) (4.7)

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9 questions

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6 sample questions

Question 1.
What does the trapezoidal rule approximate?
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Think of how this relates to shapes we know.
Question 2.
Define a function in Python that squares its input.
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What does x represent in programming?
3Question 3.
What type of shape does the trapezoidal rule use for approximation?
- Triangles
- Trapezoids
- Rectangles
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Think about the name of the rule.
4Question 4.
True or False: The trapezoidal rule can be used for functions with discontinuities.
- True
- False
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Consider how discontinuities might affect the shapes involved.
Question 5.
Using the trapezoidal rule, approximate the integral of f(x) = sin(x) from 0 to π using 10 intervals.
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Consider how the sine function behaves across this interval.
Question 6.
Create a Python function using the trapezoidal rule to approximate the integral of f(x) = e^x from 0 to 1 with 20 intervals. Discuss the results.
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Make sure to calculate the heights of the function correctly at intervals.

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