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

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

Continuity and Differentiability Exercise 5.6 Solutions

1. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx .
x = 2at2 , y = at4 

Solution

The given equations are x = 2at2 , y = at4 
 


2. If x and y are connected parametrically by the equations x = a cos θ, y = b cos θ, without eliminating the parameter, find dy/dx .

Solution

The given equations are x = a cos θ, y = b cos θ


3. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx .
x = sin t, y = cos 2t 

Solution

The given equations are x = sin t, y = cos 2t


Solution


4. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx. 
x = 4t, y = 4/y 
Solution
The given equations are x = 4t, y = 4/y 

5. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx. 
x = cos θ- cos 2θ, y = sin θ - sin 2θ
Solution
The given equations are x = cos θ- cos 2θ, y = sin θ - sin 2θ


6. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a (θ – sin θ), y = a (1 + cos θ)

Solution

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


7. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx. 
x = sin3t/√(cos 2t) , y = cos3t/√(cos 2t)

Solution

The given equations are x = sin3t/√(cos 2t) and  y = cos3t/√(cos 2t)


8. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx. 
x = a[cos t + log tan (t/2) ], y = a sin t 

Solution

The given equation are x = a[cos t + log tan (t/2) ], y = a sin t 


9. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a sec θ, y = b tan θ

Solution

The given equations are x = a sec θ, y = b tan θ


10. If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx.
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)

Solution

The given equations are x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)


11. If x = √(asin – 1), y = √(acos – 1) show that dy/dx = -y/x

Solution

The given equations are  x = √(asin – 1) and  y = √(acos – 1)

Hence, proved.

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