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Class 12

Continuity and Differentiability: Mixed Practice — Quiz

Five mixed questions across continuity and differentiation. Pick one answer for each.

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

  1. Find kk so that f(x)={kx2,x≤36,x>3f(x) = \begin{cases} kx^2, & x \le 3 \\ 6, & x > 3 \end{cases} is continuous at 33.
  2. The points of discontinuity of f(x)=x+2x2−7x+12\displaystyle f(x) = \dfrac{x + 2}{x^2 - 7x + 12} are
  3. ddxcos⁡(sin⁡x)\displaystyle \dfrac{d}{dx}\cos(\sin x) equals
  4. ddx x2x\displaystyle \dfrac{d}{dx}\,x^{2x} (for x>0x > 0) equals
  5. If x=2cos⁡θx = 2\cos\theta and y=3sin⁡θy = 3\sin\theta, then dydx\displaystyle \dfrac{dy}{dx} equals
Unanswered questions are marked wrong.

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