NCERT Class 12 · Ch 5 Exercise 5.1 · Q14
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 14
Discuss continuity and find any discontinuities of f(x)=3 for 0≤x≤1; 4 for 1<x<3; 5 for 3≤x≤10.
💡 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: Discontinuous at 1 and 3; continuous at every other point of [0,10], with one-sided endpoint continuity.
- At 1, the left limit and value are 3 but the right limit is 4. At 3, the left limit is 4 but the right limit and value are 5.
- Inside each constant interval the function is continuous. The right limit at 0 is 3=f(0), and the left limit at 10 is 5=f(10).
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