NCERT Class 12 · Ch 5 Exercise 5.1 · Q5
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 5
Is f(x)=x for x≤1 and f(x)=5 for x>1 continuous at 0,1,2?
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: Continuous at 0 and 2; discontinuous at 1.
- Near 0 the function is x, so its limit and value are 0. Near 2 it is constant 5, so both are 5.
- At 1, the left limit and f(1) are 1, while the right limit is 5. The two-sided limit fails.
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