NCERT Solutions for Chapter 5 Continuity and Differentiability Class 12 Maths 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 = √(a^{sin – 1}), y = √(a^{cos – 1}) show that dy/dx = -y/x

Solution

The given equations are  x = √(a^{sin – 1}) and  y = √(a^{cos – 1})

Hence, proved.