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Class 12 Continuity And Differentiability · Mcq Single Correct1 Markscontinuity_parameters

Class 12 Maths · Continuity And Differentiability · Mcq Single Correct #1

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 continuity at 0.

✅ Step-by-Step Solution

Final Answer: Option (B): −1
  1. The limit is k²/2 from (1−cos u)/u²→1/2 and sin x/x→1. Setting it to 1/2 gives k²=1; k<0 selects −1.

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