Class 12 Continuity And Differentiability · Short Answer2 Markspiecewise_continuity
Class 12 Maths · Continuity And Differentiability · Short Answer #116
Examine continuity of f(x)=|x|+|x−1| at x=1.
✅ Step-by-Step Solution
Final Answer: Continuous at 1.
- For x near 1 on the left, f(x)=x+(1−x)=1; on the right, f(x)=x+(x−1)=2x−1.
- The left limit is 1, the right limit is 2·1−1=1, and f(1)=1.
- Both limits equal the value, so f is continuous at 1.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] For x near 1 on the left, f(x)=x+(1−x)=1; on the right, f(x)=x+(x−1)=2x−1.
- [1 mark] The left limit is 1, the right limit is 2·1−1=1, and f(1)=1.
- [0.5 marks] Both limits equal the value, so f is continuous at 1.
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