{"id":3790,"date":"2026-06-06T22:39:26","date_gmt":"2026-06-06T17:09:26","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=3790"},"modified":"2026-06-06T22:40:13","modified_gmt":"2026-06-06T17:10:13","slug":"ncert-class-12-maths-exercise-5-1-solutions-continuity","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-12-maths-exercise-5-1-solutions-continuity\/","title":{"rendered":"NCERT Class 12 Maths Exercise 5.1 Solutions | Continuity"},"content":{"rendered":"
\"image_print\"Print<\/span><\/a> 2<\/span><\/div>\n

Short Introduction<\/h2>\n\n\n\n

Continuity is one of the most important concepts of Calculus. It helps us understand whether a function behaves smoothly around a point without any sudden breaks or jumps. In CBSE Class 12 Mathematics, Chapter 5 “Continuity and Differentiability” introduces students to the formal definition of continuity and its applications.<\/p>\n\n\n\n

Exercise 5.1 focuses on checking the continuity of polynomial, rational, modulus, piecewise and trigonometric functions at specific points.<\/p>\n\n\n\n

This complete solution guide by www.mymockmate.com<\/a><\/strong> provides easy-to-understand step-by-step explanations that are highly useful for CBSE Board Exams and competitive examinations.<\/p>\n\n\n\n

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Quick Information Box<\/h1>\n\n\n\n
Particular<\/th>Details<\/th><\/tr><\/thead>
Chapter<\/td>5<\/td><\/tr>
Chapter Name<\/td>Continuity and Differentiability<\/td><\/tr>
Exercise<\/td>5.1<\/td><\/tr>
Board<\/td>CBSE<\/td><\/tr>
Class<\/td>12<\/td><\/tr>
Difficulty Level<\/td>Easy to Moderate<\/td><\/tr>
Important For<\/td>Board Exams, JEE, CUET<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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Concepts Used (Topics Covered)<\/h1>\n\n\n\n

\u2714 Definition of Continuity<\/p>\n\n\n\n

\u2714 Left Hand Limit (LHL)<\/p>\n\n\n\n

\u2714 Right Hand Limit (RHL)<\/p>\n\n\n\n

\u2714 Existence of Function Value<\/p>\n\n\n\n

\u2714 Continuous Functions<\/p>\n\n\n\n

\u2714 Polynomial Functions<\/p>\n\n\n\n

\u2714 Rational Functions<\/p>\n\n\n\n

\u2714 Modulus Functions<\/p>\n\n\n\n

\u2714 Piecewise Functions<\/p>\n\n\n\n

\u2714 Trigonometric Functions<\/p>\n\n\n\n

\u2714 Greatest Integer Function<\/p>\n\n\n\n

\u2714 Composite Functions<\/p>\n\n\n\n

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Important Formulas<\/h1>\n\n\n\n

Definition of Continuity<\/h3>\n\n\n\n

A function f(x) is continuous at x = a if<\/p>\n\n\n\n

lim x\u2192a f(x) = f(a)<\/p>\n\n\n\n

That is,<\/p>\n\n\n\n

LHL = RHL = f(a)<\/p>\n\n\n\n

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Polynomial Functions<\/h3>\n\n\n\n

Every polynomial function is continuous for all real numbers.<\/p>\n\n\n\n

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Rational Functions<\/h3>\n\n\n\n

A rational function is continuous wherever its denominator is not zero.<\/p>\n\n\n\n

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Modulus Function<\/h3>\n\n\n\n

f(x)=|x|<\/p>\n\n\n\n

is continuous for every real number.<\/p>\n\n\n\n

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Sum, Difference and Product Rule<\/h3>\n\n\n\n

If f(x) and g(x) are continuous at x=a, then<\/p>\n\n\n\n