NCERT Class 12 · Ch 5 Exercise 5.1 · Q4
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 4
Prove f(x)=xⁿ is continuous at x=n, for a positive integer n.
💡 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 x=n.
- The limit power rule gives limₓ→ₙxⁿ=(limₓ→ₙx)ⁿ=nⁿ.
- This equals f(n), the definition of continuity.
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