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Class 11

Limits and Derivatives: Mixed Practice, Quiz

Five mixed questions on limits and derivatives. Pick one answer for each.

5 questions, one mark each. 3 to pass. Suggested time: 10 minutes. Your answers are not recorded.

  1. Find lim⁡x→4x2−5x+4x−4\displaystyle\lim_{x \to 4} \frac{x^2 - 5x + 4}{x - 4}.
  2. Find lim⁡x→0sin⁡6xsin⁡2x\displaystyle\lim_{x \to 0} \frac{\sin 6x}{\sin 2x}.
  3. Find the slope of the tangent to y=x4y = x^4 at x=−1x = -1.
  4. A particle moves with s=t3−3t2+2s = t^3 - 3t^2 + 2 metres after tt seconds. Find its velocity at t=3t = 3.
  5. Differentiate x2cos⁡xx^2\cos x.
Unanswered questions are marked wrong.

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