Sunday, May 23, 2021

CHAPTER 5 : CONTINUITY AND DIFFERENTIABILITY

 CHAPTER 5 : CONTINUITY AND DIFFERENTIABILITY

VIDEO ON HOW TO VIEW THE CONTENTS AT THIS BLOG


UNIT III – CALCULUS

Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

NCERT TEXT BOOK – CHAPTER 5

The digital copy of NCERT text book - Chapter 5 – Continuity and Differentiability for reference

https://drive.google.com/file/d/1jh3swAojksv-oDHa0iPOAFHWSzwLDpVG/view?usp=sharing

 

CONCEPTS

The handout contains definition and examples to Chapter 5 – Continuity and Differentiability

https://drive.google.com/file/d/1ZhV92Si4V2diUUqm95OojFEgS0YUIyWh/view?usp=sharing

SOLUTIONS TO NCERT TEXT BOOK QUESTIONS 

Solution to NCERT text book Exercises of Chapter 5 is solved through PPT.  The PPT is made with animation to view the steps of solutions.

EXERCISE

LINK TO OPEN PPTs ON SOLUTIONS FROM GOOGLE DRIVE

5.1 Continuity of a function


5.2 Derivative of composite function


5.3 Differentiation of implicit function


5.3 Differentiation of inverse trigonometric function


5.4 Differentiation of Exponential and Log function


5.5 Logarithmic Differentiation


5.6 Derivative of Parametric Equations


5.7 Second Ordre Derivative


5.8 Mean Value Theorem


 

SOLUTIONS WITH NARRATIONS TO NCERT TEXT BOOK QUESTIONS 

Solution with narrations to NCERT text book Exercises of Chapter 5 is solved through PPT.  The PPT is made with animation and narrations to view the steps of solutions.

EXERCISE

LINK TO OPEN PPTs ON SOLUTIONS WITH NARRATIONS FROM GOOGLE DRIVE

5.1 Continuity of a function

https://drive.google.com/file/d/1dnpB6cd-_SHg0oudtDPlxB96LZI64Ucu/view?usp=sharing

5.2 Derivative of composite function

https://drive.google.com/file/d/17AJpPymXBUlT4kzTTRWsP8kqKIicA1m6/view?usp=sharing

5.3 Differentiation of implicit function

https://drive.google.com/file/d/1i-6Z5mjXdOeuyu1bbwTRX2ykNNkwFqkr/view?usp=sharing

5.3 Differentiation of inverse trigonometric function

https://drive.google.com/file/d/1bHqiwa6iwZD6RnbXtpEpwRAGxxKOCU1c/view?usp=sharing

5.4 Differentiation of Exponential and Log function

https://drive.google.com/file/d/1ZM3xjBnSgjTpngK8mn740OJt3jT7dIo4/view?usp=sharing

5.5 Logarithmic Differentiation

https://drive.google.com/file/d/12Mj6ShrfGgaaen2134bwbihJZfRV76Z8/view?usp=sharing

5.6 Derivative of Parametric Equations

https://drive.google.com/file/d/1gCZo_jJQ_8AAfUmg6fnRgwWjuFsbif4n/view?usp=sharing

5.7 Second Order Derivative

https://drive.google.com/file/d/1twIzd-qy3N1B3EY8_3OtkKzaC-ckVJT5/view?usp=sharing

5.8 Mean Value Theorem

https://drive.google.com/file/d/11i8_G0yVDOaV5kWqkEt3ARaGjlo_gU0x/view?usp=sharing

 

SOLUTIONS TO NCERT TEXT BOOK QUESTIONS IN VIDEO FORMATS

The PPTs on Solution to Solution with narrations to NCERT text book Exercises of Chapter 5 is converted into video and the same is uploaded in YouTube.  

EXERCISE

LINK TO YOUTUBE VIDEO

5.1 Continuity of a Function

https://youtu.be/TzLzUKG-sMo

5.2 Differentiation of Composite Functions

https://youtu.be/bBK_kosk-xg

 

5.3 Differentiation of Implicit Functions

https://youtu.be/JiY0fYPkWGA

5.3 Differentiation of inverse trig functions

https://youtu.be/0EVlCe0mS60

5.4 Differentiation of Exponential and Log Functions

https://youtu.be/C25rBwflAc4

5.5 Logarithmic differentiation 

https://youtu.be/zITglEg-KPg

5.6 Differentiation of Parametric form

https://youtu.be/owARfQuD6uI

5.7 Second Order Derivative

https://youtu.be/cC35bMM5RXc

5.8 Mean Value Theorem

https://youtu.be/ok-1vsiRiH8

 

MCQ QUESTIONS ON CHAPTER 5

The document contains Multiple Choice questions on Chapter 5

https://drive.google.com/file/d/1_qq4Kj3dt6vG1mdCklGAly0cFu1eKUvn/view?usp=sharing

 

PRACTICE QUESTIONS ON CHAPTER 5

The document contains practice questions on Chapter 5

https://drive.google.com/file/d/12KwaLN4IqrXzQ_08PAFDijG4nv1MPghd/view?usp=sharing

 

LAB ACTIVITIES BY NCERT

The lab activities on Chapter 5  published by NCERT.  The document contains 6 activities 

https://drive.google.com/file/d/1asZxP1L-l0MklX5VZU8lJ1bj7sV3oSEg/view?usp=sharing

 

MATERIAL FOR FURTHER REFERENCE

S.No

Links to Videos from Swayamprabha and NROER on continuity and Diff

1

https://youtu.be/y8-ZLRfo0pE

2

https://youtu.be/CJ3mVRYdIWo

3

https://youtu.be/f7AixPfL8JM

4

https://youtu.be/GX1ax3dOEVk

5

https://youtu.be/W9L31iPKi6M

6

NROER - File - Limits and Continuity

7

NROER - File - Logarithmic Differentiation

8

NROER - File - Differentiation An Introduction

9

NROER - File - Chain Rule

10

NROER - File - Second Order Derivative

11

NROER - File - Rolle's and Mean Value Theorems

 

 

 

 

 


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Monday, April 27, 2020

CHAPTER 4 : DETERMINANTS

CHAPTER 4 : DETERMINANTS 

VIDEO ON CONTENT OF THIS PAGE


Determinants 

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

NCERT TEXT BOOK : CHAPTER 4 : DETERMINANTS 

The digital form of NCERT Book - Chapter 4 - Determinants for reference 

 https://drive.google.com/file/d/1CAP0vSmbmBDZvsmgwhaIhwcafc59Draz/view?usp=sharing

CONTENT

The document contains definition of determinants, properties of determinants, minor, cofactors and application of determinants, adjoint of a square matrix, Solution of system of linear equations by matrix method 


SOLUTIONS TO NCERT TEXT BOOK EXERCISES ON CHAPTER 4

The Power Point Presentations contain definitions with examples and solution to NCERT text book exercises on chapter 4 with animations on solution steps 


SOLUTIONS WITH NARRATIONS TO NCERT TEXT BOOK EXERCISES ON CHAPTER 4

The Power Point Presentations contain definitions with examples and solution with narrations to NCERT text book exercises on chapter 4 with animations on solution steps 


VIDEOS ON SOLUTION TO NCERT TEXT BOOK EXERCISES ON CHAPTER 4

The solution with narrations to NCERT text book exercises on Chapter 4 is converted to video and uploaded in YouTube and the link is given below

Exercise
Link to YouTube videos on solutions to NCERT Text book questions
4.1
https://youtu.be/vre4ALWgH9g
4.2

4.3

4.4
https://youtu.be/zPxXzj08q0k
4.5
https://youtu.be/0Nls-wNq1NY
4.6
https://youtu.be/SJuu1LEneIM

MCQ on Chapter 4 - DETERMINANTS 

The document contains MCQ on chapter - 4 Determinants for practice 


PRACTICE QUESTIONS

The document contains practice questions on chapter 4 and also from chapters 1 to 4 for revision 


MATERIAL FOR FURTHER REFERENCE

The link to the videos uploaded in Swayamprabha channel is given for further reference and practice 



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CHAPTER 3 MATRICES

CHAPTER 3 - MATRICES

VIDEO ON CONTENTS OF THIS BLOG


Unit-II: Algebra

1. Matrices 

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

NCERT TEXT BOOK - CHAPTER 2 - MATRICES

The digital copy of NCERT Text book - Chapter 2 - Matrices for reference 
The document contains introduction to matrices, types of matrices, operation on matrices, elementary row and column operations and its applications


Solutions to NCERT Text-book Exercises on Chapter 3 - Matrices

The solution to NCERT Text-book Exercises on chapter 3 - Matrices presented in the form of Power Point Presentations.  The PPTs contains animations to the steps of solutions to the questions 

Solutions with narations to NCERT Text-book Exercises on Chapter 3 - Matrices

The solution to NCERT Text-book Exercises on chapter 3 - Matrices presented in the form of Power Point Presentations.  The PPTs contains animations with narrations to the steps of solutions to the questions 


Videos on Solutions to NCERT Text-book Exercises on Chapter 3 - Matrices

The solution to NCERT Text-book Exercises on chapter 3 - Matrices presented in the form of videos uploaded in YouTube 

Exercise
Link to YouTube videos on solutions to NCERT Text book questions
3.1
 https://youtu.be/IlicR9bQQCc
3.2
https://youtu.be/21dcGjcJmaw
3.3
 https://youtu.be/jSLC1HNlOg0
3.4
 https://youtu.be/mzIgcHEdVlg

MCQ ON CHAPTER 3 - MATRICES 


The document contains MCQ on Chapter 3 Matrices for practice 

PRACTICE QUESTIONS ON CHAPTER 3 - MATRICES 

The documents contains practice questions on Chapter 3 - Matrices and practice item on chapters 1 to 3 for revision 


FOR FURTHER REFERENCE

The links to the videos on Matrices prepared by IIT, Delhi for Swahamprabha portal 


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