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Class 12

Continuity and Differentiability — Quiz

Five questions on continuity and differentiability at a point. Pick one answer for each.

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

  1. f(x)={2x+1,x≤3x2−2,x>3f(x) = \begin{cases} 2x + 1, & x \le 3 \\ x^2 - 2, & x > 3 \end{cases}. At x=3x = 3, ff is
  2. Find kk so that f(x)={kx+3,x≤25x−1,x>2f(x) = \begin{cases} kx + 3, & x \le 2 \\ 5x - 1, & x > 2 \end{cases} is continuous at x=2x = 2.
  3. f(x)=x2−9x−3\displaystyle f(x) = \dfrac{x^2 - 9}{x - 3} for x≠3x \ne 3 and f(3)=5f(3) = 5. What is lim⁡x→3f(x)\displaystyle \lim_{x \to 3} f(x), and is ff continuous at 33?
  4. The points of discontinuity of f(x)=x+1x2−4\displaystyle f(x) = \dfrac{x + 1}{x^2 - 4} are
  5. The function f(x)=∣x−4∣f(x) = \lvert x - 4 \rvert at x=4x = 4 is
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