Practice Central Difference Formulas - 3.4 | 3. Numerical Differentiation | Mathematics - iii (Differential Calculus) - Vol 4
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3.4 - Central Difference Formulas

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the central difference formula for the first derivative?

💡 Hint: Think about how we approximate using points around x.

Question 2

Easy

What data points are needed for the second derivative approximation?

💡 Hint: Remember you need data from both sides.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

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

Question 1

What does the central difference formula use for its calculation?

  • Only the point of interest
  • Points on both sides
  • Only previous points

💡 Hint: Think about the formula used for estimation.

Question 2

True or False: The central difference formula is less accurate than the forward difference formula.

  • True
  • False

💡 Hint: Consider how more data points influence accuracy.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the following data points: x = [1, 1.2, 1.4, 1.6, 1.8] and corresponding f(x) values = [0, 0.128, 0.544, 1.296, 2.432], apply the central difference method to estimate f′(1.6) and f′(1.4).

💡 Hint: Use the right data points and don’t forget the step-size in your calculations.

Question 2

Analyze the effect on the accuracy of the resulting derivative estimation if the spacing (h) between points is halved. Discuss how it relates to truncation and round-off errors.

💡 Hint: Consider both types of errors when adjusting h.

Challenge and get performance evaluation