Leibnitz's theorem and L'Hospital's rule

Leibnitz's theorem and L'Hospital's rule Quiz

Spec 2.3–4 · Edexcel A-Level Further Maths: Quiz

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  1. 1. In (uv)′′′(uv)''', what is the coefficient of u′′v′u''v'?

    • A. 11
    • B. 22
    • C. 33
    • D. 66

  2. 2. lim⁡x→0sin⁡3xsin⁡5x\displaystyle\lim_{x\to0}\frac{\sin3x}{\sin5x} equals

    • A. 35\frac35
    • B. 53\frac53
    • C. 11
    • D. 00

  3. 3. Which limit can L'Hospital's rule be applied to directly?

    • A. lim⁡x→0cos⁡xx\displaystyle\lim_{x\to0}\frac{\cos x}{x}
    • B. lim⁡x→01−cos⁡xx2\displaystyle\lim_{x\to0}\frac{1-\cos x}{x^2}
    • C. lim⁡x→0x+2x2+1\displaystyle\lim_{x\to0}\frac{x+2}{x^2+1}
    • D. lim⁡x→1x2x+1\displaystyle\lim_{x\to1}\frac{x^2}{x+1}

  4. 4. lim⁡x→02sin⁡x−sin⁡2xx−sin⁡x\displaystyle\lim_{x\to0}\frac{2\sin x-\sin2x}{x-\sin x} equals

    • A. 00
    • B. 22
    • C. 33
    • D. 66

  5. 5. lim⁡x→∞(1+ax)x\displaystyle\lim_{x\to\infty}\left(1+\frac ax\right)^x equals

    • A. aa
    • B. e\mathrm{e}
    • C. ea\mathrm{e}^a
    • D. 11

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