Class 12 Continuity And Differentiability · Short Answer2 Markscontinuity_parameters
Class 12 Maths · Continuity And Differentiability · Short Answer #47
Let f(x)=sin²(λx)/x² for x≠0 and f(0)=1. Find all real λ for continuity at 0.
✅ Step-by-Step Solution
Final Answer: λ=±1
- For λ≠0, write f(x)=λ²[sin(λx)/(λx)]². For λ=0 the punctured expression is identically 0.
- The limit is λ² in every case. Continuity requires λ²=f(0)=1.
- Hence λ=±1.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For λ≠0, write f(x)=λ²[sin(λx)/(λx)]². For λ=0 the punctured expression is identically 0.
- [1 mark] The limit is λ² in every case. Continuity requires λ²=f(0)=1.
- [0.5 marks] Hence λ=±1.
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