Locating roots and iteration

Locating roots and iteration Quiz

Spec 9.1–2 · Edexcel A-Level Maths: Quiz

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  1. 1. Which interval contains a root of f(x)=x3+x−3f(x)=x^3+x-3?

    • A. [0,1][0,1]
    • B. [−1,0][-1,0]
    • C. [1,2][1,2]
    • D. [2,3][2,3]

  2. 2. For f(x)=1xf(x)=\frac1x, f(−1)=−1f(-1)=-1 and f(1)=1f(1)=1. Why is there no root in [−1,1][-1,1]?

    • A. ff is not continuous at x=0x=0.
    • B. The interval is too narrow.
    • C. f(−1)f(-1) and f(1)f(1) are equal in size.
    • D. ff is a linear function.

  3. 3. For xn+1=2+1xnx_{n+1}=2+\frac{1}{x_n} with x0=2x_0=2, find x2x_2.

    • A. 2.52.5
    • B. 2.252.25
    • C. 2.22.2
    • D. 2.42.4

  4. 4. Which gradient of y=g(x)y=g(x) at the root gives a convergent staircase?

    • A. g′<−1g'<-1
    • B. 0<g′<10<g'<1
    • C. g′>1g'>1
    • D. g′>2g'>2

  5. 5. f(x)=(x−1)(x−2)f(x)=(x-1)(x-2) has f(0)=2f(0)=2 and f(3)=2f(3)=2. What can be concluded?

    • A. There is no root in [0,3][0,3].
    • B. There is exactly one root in [0,3][0,3].
    • C. Nothing: the interval has two roots so there is no sign change.
    • D. ff is not continuous.

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