Newton-raphson Method

Newton-raphson Method

What is it?

Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.

In simple words

• Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.
• Worked pattern: For x²-2, x0=1.5 gives x1=1.5+21.52=1.4167.
• Final check: domain, sign, notation, units, and reasonableness.

Important terms

Newton-Raphson method: Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.

What you should learn

• State the rule for newton-raphson method.
• Solve a newton-raphson method problem step by step.
• Check the result, restrictions, notation, and units.

Full school-level explanation

Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.

CONCEPT AND RULE

Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.

METHOD

For newton-raphson method, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.

WORKED EXAMPLE

For x²-2, x0=1.5 gives x1=1.5+21.52=1.4167.

COMMON MISTAKE

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

How to solve newton-raphson method

How it works

• Identify the mathematical objects, givens, restrictions, and required result.
• Choose and write the relevant definition, theorem, or formula.
• Substitute with brackets and carry out one justified step per line.
• Simplify, state the final answer clearly, and verify it in the original setting.

Remember

• Newton-Raphson method
• rule
• worked example
• worked example

How the ideas connect

Worked example: For x²-2, x0=1.5 gives x1=1.5+21.52=1.4167.

Deeper understanding

Go beyond memorising Newton-raphson Method. Connect the definition to reasons, relationships, exceptions, and exam wording.

How the ideas connect

Worked example: For x²-2, x0=1.5 gives x1=1.5+21.52=1.4167.

Common mistakes

Exam focus

Core Idea

Rule / Formula

Method

Worked Example

Exam focus

Quick revision

• Newton-Raphson method
• rule
• worked example
• Newton-Raphson method: Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.
• CONCEPT AND RULE: Use x(n+1)=xn-f(xn)/f'(xn); good starting values often give rapid convergence.
• METHOD: For newton-raphson method, identify the given information and required result. Select the matching d

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

For long answers on Newton-raphson Method: define clearly → explain the main parts → give one example → state one exam caution.