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Class 11

Limits and Derivatives, Course Quiz

Ten questions across the whole Limits and Derivatives course. Pick one answer for each.

10 questions, one mark each. 6 to pass. Suggested time: 20 minutes. Your answers are not recorded.

  1. Find lim⁡x→2x3−8x−2\displaystyle\lim_{x \to 2} \frac{x^3 - 8}{x - 2}.
  2. Find lim⁡x→1x2+x−2x−1\displaystyle\lim_{x \to 1} \frac{x^2 + x - 2}{x - 1}.
  3. Find lim⁡x→0sin⁡(x/3)x\displaystyle\lim_{x \to 0} \frac{\sin(x/3)}{x}.
  4. For f(x)=∣x∣x\displaystyle f(x) = \dfrac{\lvert x \rvert}{x}, what can you say about lim⁡x→0f(x)\displaystyle\lim_{x \to 0} f(x)?
  5. Differentiate 5x4−3x5x^4 - 3x.
  6. What is ddx(1x)\displaystyle \dfrac{d}{dx}\left(\dfrac{1}{x}\right)?
  7. Differentiate sin⁡x+cos⁡x\sin x + \cos x.
  8. Find the slope of the tangent to y=x3y = x^3 at x=2x = 2.
  9. A stone falls s=4.9t2s = 4.9t^2 metres in tt seconds. Find its speed at t=2t = 2.
  10. The product rule says (uv)′(uv)^\prime equals
Unanswered questions are marked wrong.

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