5.15 Further derivatives and integrals

5.15 Further derivatives and integrals Quiz

IB Maths: Analysis and Approaches HL: Quiz

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5 questions, one answer each

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  1. 1. Find ddxtan⁡(5x)\dfrac{d}{dx}\tan(5x).

    • A. sec⁡25x\sec^{2}5x
    • B. 5sec⁡25x5\sec^{2}5x
    • C. 5sec⁡5xtan⁡5x5\sec 5x\tan 5x
    • D. 51+25x2\dfrac{5}{1 + 25x^{2}}

  2. 2. Find ddx2x\dfrac{d}{dx}2^{x} at x=3x = 3.

    • A. 8ln⁡28\ln 2
    • B. 1212
    • C. 8ln⁡2\dfrac{8}{\ln 2}
    • D. 3ln⁡23\ln 2

  3. 3. Find ∫1x2+4x+13 dx\displaystyle\int\dfrac{1}{x^{2} + 4x + 13}\,dx.

    • A. arctan⁡(x+2)+C\arctan(x + 2) + C
    • B. 19arctan⁡x+29+C\dfrac{1}{9}\arctan\dfrac{x + 2}{9} + C
    • C. 13arctan⁡x+23+C\dfrac{1}{3}\arctan\dfrac{x + 2}{3} + C
    • D. ln⁡∣x2+4x+13∣+C\ln|x^{2} + 4x + 13| + C

  4. 4. Which is ddxarcsin⁡(2x)\dfrac{d}{dx}\arcsin(2x)?

    • A. 21−4x2\dfrac{2}{\sqrt{1 - 4x^{2}}}
    • B. 11−4x2\dfrac{1}{\sqrt{1 - 4x^{2}}}
    • C. 21−2x2\dfrac{2}{\sqrt{1 - 2x^{2}}}
    • D. 21+4x2\dfrac{2}{1 + 4x^{2}}

  5. 5. Express 3(x−1)(x+2)\dfrac{3}{(x - 1)(x + 2)} in partial fractions.

    • A. 1x−1+1x+2\dfrac{1}{x - 1} + \dfrac{1}{x + 2}
    • B. 3x−1−3x+2\dfrac{3}{x - 1} - \dfrac{3}{x + 2}
    • C. 1x+2−1x−1\dfrac{1}{x + 2} - \dfrac{1}{x - 1}
    • D. 1x−1−1x+2\dfrac{1}{x - 1} - \dfrac{1}{x + 2}

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