# Ex 5.1, 9

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.1, 9 Find all points of discontinuity of f, where f is defined by = , <0 & 1 , 0 Given = , <0 & 1 , 0 Case 1 At x = 0 f is continuous at x = 0 if L.H.L = R.H.L = 0 i.e. lim x 0 = lim x 0 + = 0 & 0 = 1 Thus, L.H.L = R.H.L = f(0) f is continuous at =0 Case 2 Let x = c (where c > 0) = 1 f is continuous at x = c if lim x = ( ) Thus lim x = ( ) f is continuous for =( greater than 0). f is at continuous for all real numbers greater than 0. Case 3 Let x = c (where c < 0) = = = 1 f is continuous at x = c if lim x = ( ) Thus , lim x = ( ) f is continuous for = ( c is less than 0 ) f is continuous for all real numbers less than 0. Thus, f is continuous for x R {0} Hence f(x) is continuous at all points f is continuous

Ex 5.1, 9
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Ex 5.2, 5 Important

Ex 5.2, 9 Important

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Ex 5.3, 14 Important

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Example 33 Important

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Ex 5.6, 7 Important

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Example 41 Important

Ex 5.7, 14 Important

Example 42 Important

Ex 5.8, 5 Important

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Example 45 Important

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Misc 6 Important

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Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.