# 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 𝑓 𝑥= −&2, 𝑖𝑓 𝑥≤−12&𝑥, 𝑖𝑓 −1≤𝑥≤12, 𝑖𝑓 𝑥>1 Case 1:- At x = −1 A function is continuous at x = − 1 if L.H.L = R.H.L = 𝑓 −1 i.e. limx→ −1− 𝑓 𝑥 = limx→ −1+ 𝑓 𝑥 = 𝑓 −1 And 𝑓 −2 = −2 Thus L.H.L = R.H.L = 𝑓 −2 = −2 Hence 𝒇 𝒙 is continuous at x = −𝟏 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 = 𝑓 1 i.e. limx→ 1− 𝑓 𝑥 = limx→ 1+ 𝑓 𝑥 = 𝑓 1 & 𝑓 1 = 2 1 = 2 Thus L.H.L = R.H.L = 𝑓 −2 Hence 𝒇 𝒙 is continuous at x = 1 Case 3:- For 𝑥<−1 𝑓 𝑥 = −2 Thus, 𝑓 𝑥 is a constant function . & Every constant function is continuous for all real number. Hence 𝒇 𝒙 is continuous at 𝒙<−𝟏 Case 4:- For 𝑥>1 𝑓 𝑥 = 2 Thus, 𝑓 𝑥 is a constant function . & Every constant function is continuous for all real number. Hence 𝒇 𝒙 is continuous at 𝒙>𝟏 Case 5:- For −1≤𝑥≤1 𝑓 𝑥 = 2𝑥 So, f(x) is a polynomial & Every polynomial is continuous. ⇒ 𝒇 𝒙 is continuous at −𝟏<𝒙≤𝟏 Thus, f(x) is continuous for all real numbers, i.e. f is continuous for all x ∈ R

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.