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NCERT Solutions Exercise 5.6: Continuity & Differentiability | Mathematics (Maths) Class 12 - JEE PDF Download

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NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Exercise 5.6                                                                Page No: 181 
  
If x and y are connected parametrically by the equations given in Exercise 1 to 10, without 
eliminating the parameter, find dy/dx. 
 
1.  
Solution: Given functions are  and  
   
  
=  and  
 
 =  
Now, 
  
2.  
Solution: Given functions are  and  
  
   
 
and  
 
Page 2


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Exercise 5.6                                                                Page No: 181 
  
If x and y are connected parametrically by the equations given in Exercise 1 to 10, without 
eliminating the parameter, find dy/dx. 
 
1.  
Solution: Given functions are  and  
   
  
=  and  
 
 =  
Now, 
  
2.  
Solution: Given functions are  and  
  
   
 
and  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
  
Now, 
  
3.  
Solution: Given functions are  and  
  and 
 =  
Now, 
  
4.  
Solution: Given functions are  and  
  =   
and 
   
=  
  
Page 3


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Exercise 5.6                                                                Page No: 181 
  
If x and y are connected parametrically by the equations given in Exercise 1 to 10, without 
eliminating the parameter, find dy/dx. 
 
1.  
Solution: Given functions are  and  
   
  
=  and  
 
 =  
Now, 
  
2.  
Solution: Given functions are  and  
  
   
 
and  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
  
Now, 
  
3.  
Solution: Given functions are  and  
  and 
 =  
Now, 
  
4.  
Solution: Given functions are  and  
  =   
and 
   
=  
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
Now, 
  
5.  
Solution: Given functions are  and  
  
  
  
  
And 
 
Now  
 
6.  
Solution: Given functions are  and  
Page 4


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Exercise 5.6                                                                Page No: 181 
  
If x and y are connected parametrically by the equations given in Exercise 1 to 10, without 
eliminating the parameter, find dy/dx. 
 
1.  
Solution: Given functions are  and  
   
  
=  and  
 
 =  
Now, 
  
2.  
Solution: Given functions are  and  
  
   
 
and  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
  
Now, 
  
3.  
Solution: Given functions are  and  
  and 
 =  
Now, 
  
4.  
Solution: Given functions are  and  
  =   
and 
   
=  
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
Now, 
  
5.  
Solution: Given functions are  and  
  
  
  
  
And 
 
Now  
 
6.  
Solution: Given functions are  and  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
  
 
 
=  
  =  
=  
=  
=  
 
 
Page 5


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Exercise 5.6                                                                Page No: 181 
  
If x and y are connected parametrically by the equations given in Exercise 1 to 10, without 
eliminating the parameter, find dy/dx. 
 
1.  
Solution: Given functions are  and  
   
  
=  and  
 
 =  
Now, 
  
2.  
Solution: Given functions are  and  
  
   
 
and  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
  
Now, 
  
3.  
Solution: Given functions are  and  
  and 
 =  
Now, 
  
4.  
Solution: Given functions are  and  
  =   
and 
   
=  
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
Now, 
  
5.  
Solution: Given functions are  and  
  
  
  
  
And 
 
Now  
 
6.  
Solution: Given functions are  and  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
  
 
 
=  
  =  
=  
=  
=  
 
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
7.  
Solution: Given functions are  and  
  [By quotient rule] 
=  
=  
=  
=  
And  [By quotient rule] 
=  
=  
=  
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FAQs on NCERT Solutions Exercise 5.6: Continuity & Differentiability - Mathematics (Maths) Class 12 - JEE

1. What is the difference between continuity and differentiability in calculus?
Ans. Continuity refers to the smoothness of a function at a point, where the function exists without any holes, jumps, or asymptotes. Differentiability, on the other hand, refers to the existence of the derivative of a function at a point, indicating how the function changes locally.
2. How can we determine if a function is continuous at a given point?
Ans. To check the continuity of a function at a point, we need to ensure that the function is defined at that point, the limit of the function at that point exists, and the value of the function at that point matches the value of the limit.
3. What are the conditions for a function to be differentiable at a point?
Ans. For a function to be differentiable at a point, it must be continuous at that point, and the derivative of the function must exist at that point. This means that the function should have a well-defined tangent at that point.
4. Can a function be differentiable but not continuous?
Ans. No, a function cannot be differentiable at a point if it is not continuous at that point. Differentiability implies continuity, as the function needs to be smooth and continuous for the derivative to exist.
5. How do we find the points of discontinuity for a function?
Ans. To find the points of discontinuity for a function, we look for values of x where the function is not defined, where there are jump or removable discontinuities, or where there are vertical asymptotes. These points indicate where the function is not continuous.
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