Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at Feb. 20, 2021 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

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

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Example 11

Example 7

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Ex 5.1, 24 Important

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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.