# Ex 5.1, 16

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.1, 16 Discuss the continuity of the function f, where f is defined by = &2, 1 2& , 1 1 2, >1 Case 1:- At x = 1 A function is continuous at x = 1 if L.H.L = R.H.L = 1 i.e. lim x 1 = lim x 1 + = 1 And 2 = 2 Thus L.H.L = R.H.L = 2 = 2 Hence is continuous at x = Case 1:- At x = 1 A function is continuous at x = 1 if A function is continuous at x = 1 if if L.H.L = R.H.L = 1 i.e. lim x 1 = lim x 1 + = 1 & 1 = 2 1 = 2 Thus L.H.L = R.H.L = 2 Hence is continuous at x = 1 Case 3:- For < 1 = 2 Thus, is a constant function . & Every constant function is continuous for all real number. Hence is continuous at < Case 4:- For >1 = 2 Thus, is a constant function . & Every constant function is continuous for all real number. Hence is continuous at > Case 5:- For 1 1 = 2 So, f(x) is a polynomial & Every polynomial is continuous. is continuous at < Thus, f(x) is continuous for all real numbers, i.e. f is continuous for all x R

Chapter 5 Class 12 Continuity and Differentiability

Ex 5.1, 9
Important

Ex 5.1, 13 Important

Ex 5.1, 16 Important You are here

Ex 5.1, 18 Important

Ex 5.1, 28 Important

Ex 5.1, 30 Important

Ex 5.1, 34 Important

Ex 5.2, 5 Important

Ex 5.2, 9 Important

Ex 5.2, 10 Important

Ex 5.3, 10 Important

Ex 5.3, 14 Important

Example 32 Important

Example 33 Important

Ex 5.5,6 Important

Ex 5.5, 7 Important

Ex 5.5, 11 Important

Ex 5.5, 16 Important

Ex 5.6, 7 Important

Ex 5.6, 11 Important

Example 41 Important

Ex 5.7, 14 Important

Example 42 Important

Ex 5.8, 5 Important

Example 44 Important

Example 45 Important

Example 47 Important

Misc 6 Important

Misc 15 Important

Misc 16 Important

Misc 23 Important

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 9 years. He provides courses for Maths and Science at Teachoo.