Practice Worked Example - 3.6 | 3. Numerical Differentiation | Mathematics - iii (Differential Calculus) - Vol 4
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3.6 - Worked Example

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does h represent in the context of finding a derivative using the central difference formula?

💡 Hint: Think about how we calculate the difference between points.

Question 2

Easy

Given f(2) = 4 and f(2.2) = 5, what is the approximate value of f'(2)?

💡 Hint: Use the central difference formula.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the central difference formula used for?

  • Estimating integrals
  • Estimating derivatives
  • Solving equations

💡 Hint: Recall its definition from our discussions.

Question 2

True or False: The step size (h) affects the accuracy of numerical differentiation.

  • True
  • False

💡 Hint: Think about the implications of our previous example.

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Challenge Problems

Push your limits with challenges.

Question 1

Consider a function given by the points x = [0, 1, 2, 3] and f(x) = [0, 1, 4, 9]. Use numerical differentiation to calculate the approximate value of f'(2). What do the results tell you about the behavior of the function?

💡 Hint: Consider the average slope between the points to determine the derivative at x = 2.

Question 2

Evaluate the error in your numerical differentiation for the given function values. If h = 0.5 and you find f'(2) using central difference, how would you verify the accuracy?

💡 Hint: Remember to analyze the difference between the calculated derivative and the true derivative.

Challenge and get performance evaluation