NCERT Class 12 · Ch 5 Exercise 5.1 · Q19
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 19
Show that g(x)=x−⌊x⌋ is discontinuous at every integer.
💡 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: At each integer n, left limit 1, right limit and g(n) 0.
- For n−1<x<n, floor x=n−1, so g(x)=x−n+1 and the left limit at n is 1.
- For n≤x<n+1, floor x=n, so g(n)=0 and the right limit is 0. The unequal limits give a jump at every integer.
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