Ch05. Continuity and Differentiability Class 12 Maths - 1Y

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.

CREATED: February 8, 2020 UPDATED: June 10, 2022 STATUS: Not Enrolled

Course Content

Expand All

Introduction to Course

Continuous Functions

Continuity of Functions using Limits & PDF

Assignment – 1

Expand

Topic Content

0% Complete 0/15 Steps

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

Expand

Topic Content

0% Complete 0/18 Steps

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question 8. Find the value of k, if the following function is continuous $f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases}$

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

Expand

Topic Content

0% Complete 0/14 Steps

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

Differentiation

NCERT Exercise – 5.2

Expand

Topic Content

0% Complete 0/4 Steps

Question – 1, 2, 3

Question – 4, 5

Question – 6

Question – 7, 8

Explicit and Implicit Functions

NCERT Exercise – 5.3

Expand

Topic Content

0% Complete 0/6 Steps

Question – 1, 2

Question – 3

Question – 4, 5

Question – 6

Question – 7

Question – 8

Example – 26

Example – 27

NCERT Exercise – 5.3

Expand

Topic Content

0% Complete 0/5 Steps

Question – 9

Question – 10

Question – 11, 12

Question – 13, 14

Question – 15

NCERT Exercise – 5.4

Expand

Topic Content

0% Complete 0/5 Steps

Question – 1

Question – 2, 3

Question – 4, 5

Question – 6, 7

Question – 8, 9, 10

Logarithmic Differentiation

NCERT Exercise – 5.5

Expand

Topic Content

0% Complete 0/18 Steps

Question – 2

Question – 3

Question – 1

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

Parametric Functions

NCERT Exercise – 5.6

Expand

Topic Content

0% Complete 0/11 Steps

Question – 1

Question – 2

Question – 3

Question – 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Second Order Derivatives

NCERT Exercise – 5.7

Expand

Topic Content

0% Complete 0/14 Steps

Question – 1, 2, 3, 4

Question – 5

Question – 6

Question – 7

Question – 8

Question – 9

Question – 10

Question – 11

Question – 13

Question – 14

Question 14. If $y = Ae^{mx} + Be^{nx}$ , show that $\frac{d^2{y}}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0$ .

Question – 12

Question – 15

Question – 16

Question – 17

NCERT Miscellaneous Exercise

Expand

Topic Content

0% Complete 0/22 Steps

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 15. If ${ \displaystyle (x - a)^2 + (y - b)^2 = c^2 }$ , 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.

Question – 16

Question – 17

Question – 18, 21

Question – 19

Question – 20

Question – 22

Question – 23

M A T H Y U G