Newton-Raphson method

Newton-Raphson method Quiz

Spec 9.3 · Edexcel A-Level Maths: Quiz

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  1. 1. For f(x)=x2−5f(x)=x^2-5, the Newton-Raphson formula simplifies to which of these?

    • A. xn+1=xn−52xnx_{n+1}=x_n-\frac{5}{2x_n}
    • B. xn+1=12(xn+5xn)x_{n+1}=\frac12\left(x_n+\frac{5}{x_n}\right)
    • C. xn+1=xn2−52xnx_{n+1}=\frac{x_n^2-5}{2x_n}
    • D. xn+1=2xn−5x_{n+1}=2x_n-5

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

    • A. 1.91.9
    • B. 33
    • C. 2.12.1
    • D. 2.52.5

  3. 3. What happens if f′(xn)=0f'(x_n)=0 at some stage?

    • A. xn+1x_{n+1} is undefined because the tangent is horizontal.
    • B. The method gives the root exactly.
    • C. xn+1=xnx_{n+1}=x_n.
    • D. The method always converges.

  4. 4. In Newton-Raphson, xn+1x_{n+1} is the xx-coordinate where which of these meets the xx-axis?

    • A. The curve y=f(x)y=f(x).
    • B. The normal to the curve at xnx_n.
    • C. The chord joining xnx_n and xn−1x_{n-1}.
    • D. The tangent to the curve at x=xnx=x_n.

  5. 5. f(x)=x2−7f(x)=x^2-7 and x0=3x_0=3. Find x1x_1.

    • A. 73\frac{7}{3}
    • B. 83\frac{8}{3}
    • C. 163\frac{16}{3}
    • D. 52\frac{5}{2}

Quiz