Ch05. Continuity and Differentiability Class 12 Maths

The whole chapter Continuity and Differentiability is divided into three courses. This course is the part one. In this self study course, you will learn continuity, 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. This course also has NCERT Exercise solutions, some important NCERT Examples and assignment based on NCERT Exemplar, R.D. Sharma, board's question bank etc. Please note, all three courses based on Continuity and Differentiability do not have Rolle's Theorem, Mean Value Theorem, NCERT Exercise 5.8 and questions based on them in Miscellaneous exercise.

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English Syllabus medium

Hindi + English Explanation

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Course Content

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Introduction to Course

Continuous Functions

Continuity of Functions using Limits & PDF

Assignment – 1

15 Subtopics

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Assignment – 2

18 Subtopics

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f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases}

NCERT Exercise 5.1

14 Subtopics

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NCERT Exercise – 5.2

4 Subtopics

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y = Ae^{mx} + Be^{nx}

, show that

\frac{d^2{y}}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0

NCERT Miscellaneous Exercise

22 Subtopics

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{ \displaystyle (x - a)^2 + (y - b)^2 = c^2 }

, for some c > 0, prove that

\frac{\left[ 1 + \left( \frac{dy}{dx}\right )^2 \right ]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}}

is a constant independent of a and b.

Course Content

Introduction to Course

Continuity of Functions using Limits & PDF

Assignment – 1

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10 & Question – 11

Question – 12

Question – 13

Question – 14

Question – 15

Question – 16

Assignment – 2

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Question – 12

Question – 13

Question – 14

Question – 15

Question – 16

Question – 17

Question – 18 and Question – 19

NCERT Exercise 5.1

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 17

Question – 18

Question – 20

Question – 21, 22

Question – 31

Question – 32

Question – 33

Question – 34

Question – 19

NCERT Exercise – 5.2

Question – 1, 2, 3

Question – 4, 5

Question – 6

Question – 7, 8

Explicit and Implicit Functions

NCERT Exercise – 5.3

Question – 1, 2

Question – 3

Question – 4, 5

Question – 6

Question – 7

Question – 8

Example – 26

Example – 27

NCERT Exercise – 5.3

Question – 9

Question – 10

Question – 11, 12

Question – 13, 14

Question – 15

NCERT Exercise – 5.4

Question – 1

Question – 2, 3

Question – 4, 5

Question – 6, 7

Question – 8, 9, 10