# Ex 5.1, 9 - Chapter 5 Class 12 Continuity and Differentiability (Important Question)

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Ex 5.1, 9 Find all points of discontinuity of f, where f is defined by 𝑓(𝑥)={█(𝑥/|𝑥| , 𝑖𝑓 𝑥<0@&−1 , 𝑖𝑓 𝑥≥ 0)┤ Since we need to find continuity at of the function We check continuity for different values of x When x = 0 When x > 0 When x < 0 Case 1 : When x = 0 f(x) is continuous at 𝑥 =0 if L.H.L = R.H.L = 𝑓(0) Since there are two different functions on the left & right of 0, we take LHL & RHL . if lim┬(x→0^− ) 𝑓(𝑥)=lim┬(x→0^+ ) " " 𝑓(𝑥)= 𝑓(0) LHL at x → 0 lim┬(x→0^− ) f(x) = lim┬(h→0) f(0 − h) = lim┬(h→0) f(−h) = lim┬(h→0) (−ℎ)/|−ℎ| = lim┬(h→0) (−ℎ)/ℎ = lim┬(h→0) −1 = −1 RHL at x → 0 lim┬(x→0^+ ) f(x) = lim┬(h→0) f(0 + h) = lim┬(h→0) f(h) = lim┬(h→0) −1 = −1 Now, f(0) = −1 Hence, L.H.L = R.H.L = 𝑓(0) ∴ f is continuous at x=−3 Case 2 : When x < 0 For x < 0, f(x) = 𝑥/(|𝑥|) f(x) = 𝑥/((−𝑥)) f(x) = −1 Since this constant (As x < 0, x is negative) It is continuous ∴ f(x) is continuous for x < 0 Case 3 : When x > 0 For x > 0, f(x) = −1 Since this constant It is continuous ∴ f(x) is continuous for x > 0 ∴ f is continuous for all real numbers Thus, f is continuous for 𝑥∈ R

Chapter 5 Class 12 Continuity and Differentiability

Ex 5.1, 9
Important
You are here

Ex 5.1, 13

Ex 5.1, 16

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

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

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 Questions 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.