NCERT Class 12 · Ch 5 Exercise 5.1 · Q18
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 18
Can f(x)=λ(x²−2x) for x≤0 and 4x+1 for x>0 be continuous at 0? What about 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: No λ gives continuity at 0; continuous at 1 for every λ.
- At 0 the left limit and value are 0, whereas the right limit is 1, independently of λ.
- A neighbourhood of 1 uses only 4x+1, a polynomial, so the limit equals f(1)=5.
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