The Newton-Raphson process

The Newton-Raphson process Quiz

Spec 3.1 · Edexcel International A Level Further Maths: Quiz

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  1. 1. Which is the Newton-Raphson iteration for f(x)=x2−7f(x)=x^2-7?

    • A. xn+1=xn−xn2−7xnx_{n+1}=x_n-\frac{x_n^2-7}{x_n}
    • B. xn+1=xn2−72xnx_{n+1}=\frac{x_n^2-7}{2x_n}
    • C. xn+1=xn+xn2−72xnx_{n+1}=x_n+\frac{x_n^2-7}{2x_n}
    • D. xn+1=xn2+72xnx_{n+1}=\frac{x_n^2+7}{2x_n}

  2. 2. For f(x)=x2−7f(x)=x^2-7 with x0=3x_0=3, what is x1x_1 to 3 decimal places?

    • A. 2.6672.667
    • B. 2.7502.750
    • C. 3.3333.333
    • D. 2.6462.646

  3. 3. Which starting value makes Newton-Raphson fail for f(x)=x3−3x+1f(x)=x^3-3x+1?

    • A. x0=0x_0=0
    • B. x0=0.5x_0=0.5
    • C. x0=−1x_0=-1
    • D. x0=2x_0=2

  4. 4. Geometrically, xn+1x_{n+1} is where...

    • A. the chord joining two points meets the xx-axis
    • B. the tangent at xnx_n meets the xx-axis
    • C. the normal at xnx_n meets the yy-axis
    • D. the curve meets the line y=xny=x_n

  5. 5. For f(x)=ex−4f(x)=e^x-4 with x0=1x_0=1, what is x1x_1 to 3 decimal places?

    • A. 1.3861.386
    • B. 1.4721.472
    • C. 0.5280.528
    • D. 1.2821.282

Quiz