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Class 12 Continuity And Differentiability · Long Answer3 Markscontinuity_parameters

Class 12 Maths · Continuity And Differentiability · Long Answer #122

Near x=−π/6 define f(x)=[√3sin x+cos x]/(x+π/6) off the point, and f(−π/6)=k. Find k for continuity.

✅ Step-by-Step Solution

Final Answer: k=2
  1. Let h=x+π/6 so x=−π/6+h. The numerator equals 2sin(x+π/6)=2sin h.
  2. The punctured expression is 2sin h/h.
  3. Its limit as h→0 is 2; continuity requires k to equal that limit.
  4. Therefore k=2.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let h=x+π/6 so x=−π/6+h. The numerator equals 2sin(x+π/6)=2sin h.
  • [1 mark] The punctured expression is 2sin h/h.
  • [1 mark] Its limit as h→0 is 2; continuity requires k to equal that limit.
  • [0.5 marks] Therefore k=2.

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