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

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NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
Page 2


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
Page 3


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
=  
5.  
Solution:  Consider  
 
Apply derivation: 
 
  [Using Quotient Rule] 
  
  
 =  
Page 4


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
=  
5.  
Solution:  Consider  
 
Apply derivation: 
 
  [Using Quotient Rule] 
  
  
 =  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
   
=  
6.  
Solution:  Consider  ……….(i) 
 
Reduce the functions into simplest form, 
 
  
=  =  
And  
=  =  
Now, we are available with the equation below: 
   
Page 5


 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
Miscellaneous Exercise                                              Page No: 191 
 
Differentiate with respect to x the functions in Exercises 1 to 11. 
1.  
Solution:  Consider  
  
 
   
  
2.  
Solution:  Consider   
or y =  
  
   
=  
3.  
Solution:  Consider  
 
Taking log both the sides, we get 
 
  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
  
Derivate above function: 
  
  
  
  
  
 (using value of y) 
4.  
Solution:  Consider   
or  y =  
 
Apply derivation: 
  
=  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
 
=  
5.  
Solution:  Consider  
 
Apply derivation: 
 
  [Using Quotient Rule] 
  
  
 =  
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
   
=  
6.  
Solution:  Consider  ……….(i) 
 
Reduce the functions into simplest form, 
 
  
=  =  
And  
=  =  
Now, we are available with the equation below: 
   
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 5 Continuity and 
Differentiability 
=  
  
 =  
Apply derivation: 
 
  
7.  
Solution:  Consider  ……….(i) 
 
Taking log both sides: 
  =  
Apply derivation: 
 
  
  
  
=  
  
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FAQs on NCERT Solutions Miscellaneous Exercise: Continuity and Differentiability - Mathematics (Maths) Class 12 - JEE

1. What is the significance of continuity in mathematics?
Ans. Continuity in mathematics ensures that a function is smooth and has no abrupt changes or breaks. It allows us to predict the behavior of a function at any point within its domain.
2. How is continuity different from differentiability?
Ans. Continuity of a function at a point guarantees that the function exists and is well-behaved at that point. Differentiability, on the other hand, goes a step further by ensuring the existence of the derivative at that point.
3. Can a function be continuous but not differentiable?
Ans. Yes, a function can be continuous at a point but not differentiable at that point if it has a sharp corner, cusp, or vertical tangent. An example of this is the absolute value function at x = 0.
4. How do we check for continuity of a function at a point?
Ans. To check for continuity of a function at a point, we need to ensure that the function exists at that point, the limit of the function as it approaches that point exists, and the value of the function at that point matches the limit.
5. What are the common types of discontinuities in functions?
Ans. The common types of discontinuities in functions include jump discontinuities, infinite discontinuities, removable discontinuities, and oscillating discontinuities. Each type has different characteristics that affect the continuity and differentiability of the function.
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