Continuity & Differentiability
Created by Ridhi Arora, Last Updated 05Sep2019, Language:English
Continuity & Differentiability
Simply Easy Learning
Created by Ridhi Arora, Last Updated 05Sep2019, Language:English
Description
Calculus is used in every branch of the physical sciences, actuarial science, statistics, engineering and in other fields wherever a problem can be mathematically modele and an optimal solution is desired.Continuity of functions is one of the core concepts of topology.A continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output while a differentiable function of one real variable is a function whose derivative exists at each point in its domain.This video series is based on Continuity And Differentiability for class 12 students for board level and IIT JEE Mains.
Audience
These video classes have been designed for Class 12 students (Nonmedical students and commerce students with Mathematics), those who are preparing for CBSE and other Board Exams for Intermediate, +2 and IIT JEE entrance exams. These classes will also be helpful for students in preparing them for Competitive Examinations for Engineering Institutes like IIT JEE etc.
Course Content

Continuity & Differentiability
8 Lectures 00:41:20
Continuity & Differentiability Syllabus
Preview00:08:10 
Recap of Limits
Preview00:06:02 
Overview of Continuity
00:06:59 
Conditions of Continuity
00:05:33 
Removable Discontinuity
00:05:02 
Irremovable Discontinuity Part 1
00:03:33 
Irremovable Discontinuity Part 2
00:04:09 
Left Continuous & Right Continuous Function
00:01:52


Algebra of Continuous Functions
7 Lectures 00:20:09
Sum of Continuous Functions
Preview00:03:30 
Difference of Continuous Functions
Preview00:02:26 
Product of Continuous Function
00:02:03 
Product of Continuous Functions
00:02:09 
1/F Is Continuous At X = A, If F(A) ≠ 0
00:02:39 
Quotient Of 2 Continuous Functions
00:03:09 
Composition of Functions
00:04:13


Problems On Continuity
6 Lectures 00:34:45
Continuity Problem 1
00:04:40 
Continuity Problem 2
00:07:55 
Continuity Problem 3
00:05:43 
Continuity Problem 4
00:05:48 
Continuity Problem 5
00:05:49 
Continuity Problem 6
00:04:50


Always Continuous Functions
10 Lectures 00:47:06
Constant Function
Preview00:05:27 
Identity Function
00:04:20 
Polynomial Function
00:07:42 
Rational Function
00:04:14 
Modulus Function
00:02:27 
Exponential Function
00:04:29 
Logarithmic Function
00:02:40 
Trigonometric Function  Sine Function
00:07:10 
Trigonometric Function  Tangent Function
00:04:49 
Inverse Trigonometric Functions
00:03:48


Miscellaneous Problems On Continuity
5 Lectures 00:32:59
Continuity  Miscellaneous Problem 1
00:07:57 
Continuity  Miscellaneous Problem 2
00:05:25 
Continuity  Miscellaneous Problem 3
00:03:31 
Continuity  Miscellaneous Problem 4
00:08:48 
Continuity  Miscellaneous Problem 5
00:07:18


Differentiability
11 Lectures 01:01:15
Definition Of Differentiability
00:06:17 
Geometrical Meaning Of Differentiability
00:07:32 
Theorem On Differentiability
00:06:24 
Differentiability Problem 1
00:04:33 
Differentiability Problem 2
00:04:54 
Differentiability Problem 3
00:06:35 
Useful Results On Differentiability
00:05:34 
Continuity & Differentiability Problem 1
00:03:35 
Continuity & Differentiability Problem 2
00:04:43 
Derivative Of F At X For F(X)
00:04:01 
Problem On Differentiable Function
00:07:07


Differentiation
5 Lectures 00:23:33
Standard Formulas
00:04:32 
Product Rule Part 1
00:04:15 
Product Rule Part 2
00:03:42 
Quotient Rule
00:04:01 
Problems On Differentiation
00:07:03


Composition Of Functions
8 Lectures 00:54:23
Overview of Composition of Functions
Preview00:03:53 
Substitution Method Problem 1
00:06:15 
Substitution Method Problem 2
00:07:48 
Composition of Functions  Problem 1 on Chain Rule
00:08:20 
Composition of Functions  Problem 2 on Chain Rule
00:07:04 
Composition of Functions  Problem 3 on Chain Rule
00:06:00 
Composition of Functions  Problem 4 on Chain Rule
00:05:44 
Composition of Functions  Problem 5 on Chain Rule
00:09:19


Inverse Trigonometric Functions Differentiation
10 Lectures 00:52:29
Differentiation of Sin ^{1} x
00:04:58 
Differentiation of Cos ^{1} x
00:04:06 
Differentiation of Tan ^{1} x
00:04:06 
Differentiation of Cot ^{1} x
00:03:56 
Differentiation of Sec ^{1} x
00:09:15 
Differentiation of Cosec ^{1} x
00:07:25 
Inverse Trigonometric Function Problem 1
00:03:14 
Inverse Trigonometric Function Problem 2
00:04:48 
Inverse Trigonometric Function Problem 3
00:07:32 
Inverse Trigonometric Function Problem 4
00:03:09


Implicit Functions Differentiation
6 Lectures 00:32:40
Implicit Functions Overview
00:03:49 
Implicit Functions Problem 1
00:05:40 
Implicit Functions Problem 2
00:06:17 
Implicit Functions Problem 3
00:04:30 
Implicit Functions Problem 4
00:06:55 
Implicit Functions Problem 5
00:05:29


Exponential & Logarithmic Functions
1 Lectures 00:09:18
Concept of Exponential & Logarithmic Functions
00:09:18


Logarithmic Differentiation
5 Lectures 00:22:28
Logarithmic Differentiation Overview
00:04:25 
Logarithmic Differentiation Problem 1
00:04:39 
Logarithmic Differentiation Problem 2
00:05:08 
Logarithmic Differentiation Problem 3
00:04:28 
Logarithmic Differentiation Problem 4
00:03:48


Differentiation of Infinite Series
4 Lectures 00:17:18
Differentiation of Infinite Series Overview
00:02:25 
Differentiation Of Infinite Series Problem 1
00:04:24 
Differentiation Of Infinite Series Problem 2
00:06:38 
Differentiation Of Infinite Series Problem 3
00:03:51


Differentiation of Parametric Functions
4 Lectures 00:17:01
Differentiation of Parametric Functions Overview
Preview00:03:13 
Differentiation of Parametric Functions Problem 1
00:04:20 
Differentiation of Parametric Functions Problem 2
00:03:33 
Differentiation of Parametric Functions Problem 3
00:05:55


Higher Order Derivatives
5 Lectures 00:23:43
Higher Order Derivatives Overview
00:05:28 
Higher Order Derivatives Problem 1
00:05:11 
Higher Order Derivatives Problem 2
00:04:40 
Higher Order Derivatives Problem 3
00:03:08 
Higher Order Derivatives Problem 4
00:05:16


Differentiation Using Trigonometric Substitutions
4 Lectures 00:13:06
Differentiation Using Trigonometric Substitutions Overview
00:03:21 
Differentiation Using Trigonometric Substitutions Problem 1
00:03:06 
Differentiation Using Trigonometric Substitutions Problem 2
00:02:39 
Differentiation Using Trigonometric Substitutions Problem 3
00:04:00


Differentiation of One Function With Respect To Another
3 Lectures 00:13:03
Differentiation of One Function With Respect To Another Overview
00:01:54 
Differentiation Of One Function With Respect To Another Problem 1
00:05:20 
Differentiation Of One Function With Respect To Another Problem 2
00:05:49


Rolle's Theorem
7 Lectures 00:26:49
Rolle's Theorem Overview
00:02:50 
Geometrical Interpretation
00:03:07 
Algebraic Interpretation
00:03:27 
Important Results
00:04:08 
Rolle's Theorem Problem 1
00:03:11 
Rolle's Theorem Problem 2
00:06:00 
Rolle's Theorem Problem 3
00:04:06


Lagrange’s Mean Value Theorem
4 Lectures 00:22:31
Lagrange’s Mean Value Theorem Overview
Preview00:02:20 
Geometrical Interpretation Of LMV
00:05:44 
Lagrange’s Mean Value Theorem Problem 1
00:09:15 
Lagrange’s Mean Value Theorem Problem 2
00:05:12


Miscellaneous Problems On Differentiation
4 Lectures 00:15:57
Differentiation  Miscellaneous Problem 1
00:04:36 
Differentiation  Miscellaneous Problem 2
00:02:43 
Differentiation  Miscellaneous Problem 3
00:04:13 
Differentiation  Miscellaneous Problem 4
00:04:25


IIT JEE Exams Questions
10 Lectures 00:48:31
Continuity & Differentiability  IIT JEE Problem 1
00:05:19 
Continuity & Differentiability  IIT JEE Problem 2
00:05:37 
Continuity & Differentiability  IIT JEE Problem 3
00:07:46 
Continuity & Differentiability  IIT JEE Problem 4
00:03:34 
Continuity & Differentiability  IIT JEE Problem 5
Preview00:04:57 
Continuity & Differentiability  IIT JEE Problem 6
00:03:27 
Continuity & Differentiability  IIT JEE Problem 7
00:03:01 
Continuity & Differentiability  IIT JEE Problem 8
00:03:30 
Continuity & Differentiability  IIT JEE Problem 9
00:07:47 
Continuity & Differentiability  IIT JEE Problem 10
00:03:33

Ridhi Arora
Ridhi Arora holds a B. Tech Honors  Gold medalist in Computer Science. Ridhi is an ardent learner, a keen observer and a passionate Mathematics faculty for classes 11,12 and IIT JEE Mains. She is among the top 10 most viewed writers in Kota, Rajasthan, on Quora. Ridhi is also associated with Ganit Hub as Algebra HOD and Miracle Live Coaching Private Limited as a Mathematics faculty. Ridhi is a confident and dynamic trainer with a total teaching experience of 5+ years.