NCERT Class 12 · Ch 5 Exercise 5.1 · Q23
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 23
Find all discontinuities of f(x)=sin x/x for x<0 and x+1 for x≥0.
💡 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: None; f is continuous on R.
- The quotient is continuous for negative x and the polynomial for positive x.
- At 0 the left limit is lim sin x/x=1, the right limit is 1 and f(0)=1. Thus the junction is continuous.
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