NCERT Class 12 · Ch 5 Exercise 5.1 · Q3
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 3
Examine continuity: (a) x−5; (b) 1/(x−5), x≠5; (c) (x²−25)/(x+5), x≠−5; (d) |x−5|.
💡 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: (a),(d): all real x. (b): R∖{5}. (c): R∖{−5}; the missing point is removable.
- (a) A polynomial is continuous everywhere. (b) A quotient of continuous functions is continuous wherever its denominator is nonzero.
- (c) Factor x²−25=(x−5)(x+5); the quotient equals x−5 on its stated domain and is continuous there. At −5 it is undefined; assigning −10 would fill the hole.
- (d) Absolute value is continuous and composition preserves continuity.
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