NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 5 Continuity and Differentiability - Future Study Point

NCERT Solutions for Class 12 Maths Exercise 5.6 of Chapter 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

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.

exercise 5.6 continuity and differentiability

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

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Exercise 5.6-Continuity and Differentiability

 

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

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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

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

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Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
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Chapter 3- Coordinate GeometryChapter 11-Construction
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Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
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Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
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Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
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Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

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Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
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Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
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Chapter 7- Integrals
Chapter 8-Application of Integrals

 

 

 

 

 

 

 

 

 

 

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