# Example 12 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Jan. 3, 2020 by Teachoo

Last updated at Jan. 3, 2020 by Teachoo

Transcript

Example 12 Discuss the continuity of the function defined by ๐(๐ฅ)={โ(& ๐ฅ+2, ๐๐ ๐ฅ<0@&โ๐ฅ+2, ๐๐ ๐ฅ>0)โค ๐(๐ฅ)={โ(& ๐ฅ+2, ๐๐ ๐ฅ<0@&โ๐ฅ+2, ๐๐ ๐ฅ>0)โค Here, function is not defined for x = 0 So, we do not check continuity there We check continuity for different values of x When x < 0 When x > 0 Case 1 : When x < 0 For x < 0, f(x) = x + 2 Since this a polynomial It is continuous โด f(x) is continuous for x < 0 Case 3 : When x > 0 For x > 0, f(x) = โx + 2 Since this a polynomial It is continuous โด f(x) is continuous for x > 0 Hence, ๐ is continuous for all Real points except 0. Thus, ๐ is continuous for ๐ โ๐โ{๐}

Checking continuity using LHL and RHL

Example 12
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Example 10

Example 13

Ex 5.1, 10

Ex 5.1, 11

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Example 11

Example 7

Ex 5.1 ,3 Important

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Ex 5.1, 15 Important

Ex 5.1 ,7 Important

Ex 5.1, 25

Ex 5.1, 23

Ex 5.1, 24 Important

Ex 5.1 ,8

Ex 5.1, 9 Important

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Ex 5.1, 28 Important

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Ex 5.1, 30 Important

Example 15

Chapter 5 Class 12 Continuity and Differentiability

Concept wise

- Checking continuity at a given point
- Checking continuity at any point
- Checking continuity using LHL and RHL
- Algebra of continous functions
- Continuity of composite functions
- Checking if funciton is differentiable
- Finding derivative of a function by chain rule
- Finding derivative of Implicit functions
- Finding derivative of Inverse trigonometric functions
- Finding derivative of Exponential & logarithm functions
- Logarithmic Differentiation - Type 1
- Logarithmic Differentiation - Type 2
- Derivatives in parametric form
- Finding second order derivatives - Normal form
- Finding second order derivatives- Implicit form
- Proofs
- Verify Rolles theorem
- Verify Mean Value Theorem

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.