NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability will clear your doubts on the concept of Continuity and Differentiability that help you in preparing your worksheet, doing your homework, and class assignments of maths.NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability are created by Future Study Point for boosting your preparation of the CBSE Board Maths question paper 2021-22.NCERT  Solutions of Maths class 12  are the best study materials for clearing your concept on Continuity and Differentiability.

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

You can also study

What is differentiation?

Continuity and Differentiability of a function

Exercise 5.1-Continuity and Differentiability

Exercise 5.2-Continuity and Differentiability

Exercise 5.3-Continuity and Differentiability

Exercise 5.4 – Continuity and Differentiability

Exercise 5.5-Continuity and Differentiability

Exercise 5.6-Continuity and Differentiability

 

NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

If x and y are connected parametrical by the equations given in the exercise 1 to 10 ,without eliminating the parameter, find dy/dx.

Q1. x = 2at², y = at⁴

Ans. The functions are  x = 2at², y = at⁴

Taking  x = 2at²

Differentiating the function with respect to t

Taking  y = at⁴

Differentiating the function with respect to t

Dividing equation (ii) by the equation (i)

Q2.x =  acosθ, y = bcosθ

Ans. Taking x = acosθ

Differentiating the given function with respect to θ

Taking y = bcosθ

Differentiating the given function with respect to θ

Dividing equation (ii) by the equation (i)

Q3. x = sin t, y = cos 2t

Ans. Taking x = sin t

Differentiating the given function with respect to t

Taking y = cos 2t

Dividing equation (ii) by the equation (i)

Ans. Taking x = 4t

Taking

…….(ii)

Dividing equation (ii) by the equation (i)

Q5. x = cos θ – cos 2θ, y =sin θ – sin 2θ

Ans. The given functions are  x = cos θ – cos 2θ, y =sin θ – sin 2θ

Taking x = cos θ – cos 2θ

Taking y =sin θ – sin 2θ

Dividing equation (ii) by the equation (i)

Q6. x = a(θ – sin θ), y = a(1 + cos θ)

Ans.The given functions are x = a(θ – sin θ), y = a(1 + cos θ)

Taking x = a(θ – sin θ)

Differentiating the function with respect to x

Taking y = a(1 + cos θ)

Differentiating the function with respect to x

Dividing equation (ii) by the equation (i)

Ans. The given functions are

Taking

Differentiating the function with respect to t

 

Taking

Differentiating the function with respect to t

Multiplying  numerator and denominator by √(cos2t)

Dividing equation (ii) by the equation (i)

Q8.x = a(cost + log tan t/2), y = a sin t

Ans. The given functions are x = a(cost + log tan t/2), y = a sin t

Taking x = a(cost + log tan t/2)

Differentiating the function with respect to x

 

Taking y = a sin t

Differentiating the function with respect to t

Dividing equation (ii) by the equation (i)

Q9. x = a sec θ, y = b tan θ

Ans. The given functions are x = a sec θ, y = b tan θ

Taking x = a sec θ

Differentiating the function with respect to θ

Taking y = b tan θ

Differentiating the function with respect to θ

Dividing equation (ii) by the equation (i)

Q10. x = a(cos θ + θ sin θ), y = a (sinθ – θ cos θ)

Ans. Taking x = a(cos θ + θ sin θ)

Differentiating the function with respect to θ

Taking y = a (sinθ – θ cos θ)

Differentiating the function with respect to θ

Dividing equation (ii) by the equation (i)

Show that dy/dx = -y/x

Ans. Taking     

Differentiating the function with respect to t

Taking

Differentiating the function similarly as above,we get

Dividing equation (ii) by the equation (i)

Substituting the values , 

, Hence proved

You can compensate us by donating any amount of money for our survival

Our Paytm NO 9891436286

NCERT Solutions of  Science and Maths for Class 9,10,11 and 12

NCERT Solutions of class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions of class 9 science 

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

NCERT Solutions of class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT solutions of class 10 science

Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals	Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds	Chapter 12- Electricity
Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process	Chapter 14-Sources of Energy
Chapter 7-Control and Coordination	Chapter 15-Environment
Chapter 8- How do organisms reproduce?	Chapter 16-Management of Natural Resources

Solutions of class 10 last years Science question papers

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Latest sample paper of science

NCERT solutions of class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions of class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals