Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Continuity And Differentiability · Long Answer3 Markscontinuity_parameters

Class 12 Maths · Continuity And Differentiability · Long Answer #61

Let f(x)=k sin[(π/2)(x+1)] for x≤0, and f(x)=(tan x−sin x)/x³ for x>0 near 0. Find k for continuity at 0.

✅ Step-by-Step Solution

Final Answer: k=1/2
  1. From the left, f(0)=k sin(π/2)=k and the limit equals k.
  2. For the right branch, tan x−sin x=sin x(1−cos x)/cos x.
  3. The quotient becomes [sin x/x][(1−cos x)/x²]/cos x, tending to 1·(1/2)/1=1/2.
  4. Continuity requires k=1/2.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] From the left, f(0)=k sin(π/2)=k and the limit equals k.
  • [1 mark] For the right branch, tan x−sin x=sin x(1−cos x)/cos x.
  • [1 mark] The quotient becomes [sin x/x][(1−cos x)/x²]/cos x, tending to 1·(1/2)/1=1/2.
  • [0.5 marks] Continuity requires k=1/2.

Master Chapter 5: Continuity And Differentiability

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Show f(x)=2x−|x| is continuous but not differentiable at 0.
Next Question →
Let f(x)=[sin((a+1)x)+2sin x]/x for x 0 near 0. Find a,b for…

More Practice Questions in Continuity And Differentiability

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Continuity And Differentiability

Class 12 Continuity And Differentiability · Mcq Single Correct
For k<0, define f(x)=(1−cos(kx))/(x sin x) for nonzero x near 0, and f(0)=1/2. Find k for…
Class 12 Continuity And Differentiability · Mcq Single Correct
Near π/2, f(x)=k cos x/(π−2x) for x≠π/2 and f(π/2)=3. Find k for continuity.
Class 12 Continuity And Differentiability · Mcq Single Correct
Find the full set of real inputs excluded from the natural domain of cot x (its poles).
Class 12 Continuity And Differentiability · Mcq Single Correct
How many real inputs are excluded from the original formula f(x)=(x−1)/[x(x²−1)]?
Class 12 Continuity And Differentiability · Mcq Single Correct
For x≠0, f(x)=(e^(3x)−e^(−5x))/x, and f(0)=k. Find k for continuity at 0.
Class 12 Continuity And Differentiability · Mcq Single Correct
Let f(x)=x/|x| for x<0 and f(x)=−1 for x≥0. What is its complete continuity set?