NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

The document NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Continuity & Differentiability

Question 1: Find the second order derivatives of the function.

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

Answer
Let y = NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Question 2: Find the second order derivatives of the function. x20

Answer
Let y = x20
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

Question 3: Find the second order derivatives of the function. x.cos x

Answer
Let y = x.cos x
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Question 4: Find the second order derivatives of the function. log x

Answer
Let y = log x
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

Question 5: Find the second order derivatives of the function. x3 log x

Answer
Let y = x3 log x
Then,
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

Question 6: Find the second order derivatives of the function. NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

Answer

Let y = NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

 

Question 7: Find the second order derivatives of the function.

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
Let y = NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Question 8: Find the second order derivatives of the function.

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
Let y = NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

 

Question 9: Find the second order derivatives of the function.

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
Let y = NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Question 10: Find the second order derivatives of the function.

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
Let y = NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
 

Question 11: If NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
It is given that, NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Hence, proved.


Question 12:
 If  
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev  in terms of y alone.


Answer
It is given that, NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Question 13:
 If 
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
It is given that,  NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Hence, proved.

Question 14:
 If 
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev, show that  NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
It is given that, NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Hence, proved.


Question 15:
 If 
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev , show that  NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
It is given that, NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Hence, proved.


Question 16:
 If  
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev, show that NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
The given relationship is NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Taking logarithm on both the sides, we obtain

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Differentiating this relationship with respect to x, we obtain
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Hence, proved.


Question 17:
 If 
NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev, show that NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev


Answer
The given relationship is NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev
Then,

NCERT Solutions - Continuity & Differentiability, Exercise 5.7 JEE Notes | EduRev 
Hence, proved.

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