NCERT Class 12 · Ch 5 Exercise 5.1 · Q11
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 11
Discuss continuity and find any discontinuities of f(x)=x³−3 for x≤2; x²+1 for x>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: No discontinuities.
- At 2, the left limit and f(2) are 8−3=5; the right limit is 4+1=5.
- Equality of these values establishes continuity at the junction; elsewhere use polynomial continuity.
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