Practice Newton-Raphson Method - 5.1.3.3 | 5. Solution of Algebraic and Transcendental Equations | Mathematics - iii (Differential Calculus) - Vol 4
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5.1.3.3 - Newton-Raphson Method

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the formula for the Newton-Raphson method?

💡 Hint: Remember it's the current guess minus the function value divided by the derivative.

Question 2

Easy

What do you need to calculate to apply the Newton-Raphson method?

💡 Hint: Think about evaluating the slope of the function.

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 is the primary advantage of the Newton-Raphson method?

  • It always finds a root.
  • It converges quickly when near the root.
  • It requires more initial guesses.

💡 Hint: Evaluate the options based on the speed of convergence.

Question 2

True or False: The Newton-Raphson method can work without the derivative.

  • True
  • False

💡 Hint: Think about how the method is defined and its necessity for derivatives.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Apply the Newton-Raphson method to approximate the root of the equation x^3 - x - 2 = 0 starting from an initial guess of x0 = 1. Show detailed calculations for three iterations.

💡 Hint: Make sure to calculate both f(x) and f'(x) correctly at each iteration.

Question 2

Using the equation sin(x) - x/2 = 0, find the root starting with x0 = 1. Illustrate the iterations clearly until convergence is evident.

💡 Hint: Consider using a calculator for the sin function and be careful with radians.

Challenge and get performance evaluation