NCERT Solutions Class 12

NCERT Solutions Class 12

Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 7)

Exercise 5.7

Find the second order derivatives of the functions given in Exercises 1 to 5.

1. 

Ans.  Let 

 

 


2.  

Ans. Let 

 

 


3.  

Ans. Let 

  = 

 


4.  

Ans. Let 

 

       

  = 


5.  

Ans. Let 

 

 


Find the second order derivatives of the functions given in Exercises 6 to 10.

6.  

Ans. Let 

 

 


7.  

Ans. Let 

 

 = 

 


8.  

Ans. Let 

 

 

 = 


9.  

Ans.  Let 

  

 


10.  

Ans. Let 

 

 = 

 


11. If  prove that  

Ans. Let   …….(i)

 

 

 =  [From eq. (i)]


12. If  Find  in terms of  alone.

Ans. Given: 

    ……….(i)

 

 [From eq. (i)]

 ……….(ii)

 

[From eq. (ii)]


13. If  show that  

Ans. Given:      ….(i)

 

   = 

  

Now 

 

 

 

   [From eq. (i)]

  Hence proved.


14. If  show that  

Ans.  Given:     ….(i)

To prove: 

   

          ….(ii)

Again   
   ….(iii)

Now,   L.H.S.=

= 0

= R.H.S.            Hence proved.


 

15. If  show that  

Ans. Given: ……….(i)

  = 

  = 

 

  [From eq. (i)]

  =   Hence proved.


NCERT Solutions class 12 Maths Exercise 5.7

16. If  show that  

Ans. Given: 

 

Taking log on both sides,      

 

  = 

And   

 

Now, L.H.S. = 

And R.H.S. = 

 L.H.S. = R.H.S.         Hence proved.


 

17. If  show that  

Ans. Given:       ……….(i)

  

And 

  

Again  differentiating both sides w.r.t. 

 

        Hence proved.

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