NCERT Class 12 · Ch 5 Exercise 5.1 · Q24
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 24
Is f(x)=x² sin(1/x) for x≠0, f(0)=0 continuous?
💡 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: Yes, on all of R.
- For x≠0 composition and products preserve continuity.
- At 0, |x²sin(1/x)|≤x², whose limit is 0. The squeeze theorem gives lim f(x)=0=f(0).
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