Iteration and Newton-Raphson

Iteration and Newton-Raphson Quiz

Spec I2 · AQA A-Level Maths: Quiz

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  1. 1. xn+1=xn+6x_{n+1}=\sqrt{x_n+6}, x0=1x_0=1. Find x1x_1 to 3 d.p.

    • A. 2.4492.449
    • B. 2.6462.646
    • C. 77
    • D. 4949

  2. 2. The Newton-Raphson iteration for f(x)=x2−5f(x)=x^2-5 is

    • A. xn+1=xn+xn2−52xnx_{n+1}=x_n+\frac{x_n^2-5}{2x_n}
    • B. xn+1=xn−2xnxn2−5x_{n+1}=x_n-\frac{2x_n}{x_n^2-5}
    • C. xn+1=xn−(xn2−5)x_{n+1}=x_n-(x_n^2-5)
    • D. xn+1=xn−xn2−52xnx_{n+1}=x_n-\frac{x_n^2-5}{2x_n}

  3. 3. An iteration has g′(α)=0.4g'(\alpha)=0.4. The cobweb or staircase diagram is

    • A. a staircase converging to α\alpha
    • B. a cobweb converging to α\alpha
    • C. diverging from α\alpha
    • D. a closed loop around α\alpha

  4. 4. Newton-Raphson cannot be used at xnx_n when

    • A. f(xn)>0f(x_n)>0
    • B. f(xn)=1f(x_n)=1
    • C. f′(xn)=0f'(x_n)=0
    • D. xn<0x_n<0

  5. 5. For f(x)=x3−10f(x)=x^3-10 and x0=2x_0=2, find x1x_1 to 4 d.p. using Newton-Raphson.

    • A. 1.83331.8333
    • B. 2.50002.5000
    • C. 2.00002.0000
    • D. 2.16672.1667

Quiz