NCERT Class 12 · Ch 5 Exercise 5.1 · Q12
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 12
Discuss continuity and find any discontinuities of f(x)=x¹⁰−1 for x≤1; x² for x>1.
💡 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: x=1 only.
- At 1, the left limit and f(1) are 0, while the right limit is 1.
- The junction is discontinuous; the two polynomial branches are continuous away from 1.
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