Newton-Raphson (AQA A-Level Mathematics): Quizzes

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Newton-Raphson
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What type of technique is the Newton-Raphson method?

Iterative numerical technique

What is the Newton-Raphson iterative formula?

xn+1=xn−f(xn)f′(xn)x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

In the Newton-Raphson formula, what does f′(x)f'(x) represent?

The derivative of f(x)f(x)

What does xn+1x_{n+1} represent in the Newton-Raphson method?

The next approximation

What geometric concept is the Newton-Raphson formula derived from?

Tangent line to the curve

What is the convergence criterion for stopping iterations?

∣xn+1−xn∣<ϵ|x_{n+1} - x_n| < \epsilon

For f(x)=x3−2x−5f(x) = x^3 - 2x - 5 with x0=2x_0 = 2, what is x1x_1?

2.12.1

When does the Newton-Raphson method converge quickly?

Initial guess close to actual root

When can the Newton-Raphson method fail or converge slowly?

When f′(x)f'(x) is close to zero

What can affect whether the method converges to the correct root?

Choice of initial guess x0x_0

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