JEE  >  Mathematics For JEE  >  NCERT Solutions Exercise 5.7: Continuity & Differentiability

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

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Continuity & Differentiability

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

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

Answer
Let y = NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


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

Answer
Let y = x20
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

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

Answer
Let y = x.cos x
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


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

Answer
Let y = log x
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

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

Answer
Let y = x3 log x
Then,
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

Question 6: Find the second order derivatives of the function. NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

Answer

Let y = NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

 

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

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
Let y = NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


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

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
Let y = NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

 

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

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
Let y = NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


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

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
Let y = NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
 

Question 11: If NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
It is given that, NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Hence, proved.


Question 12:
 If  
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE  in terms of y alone.


Answer
It is given that, NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Question 13:
 If 
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
It is given that,  NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Hence, proved.

Question 14:
 If 
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE, show that  NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
It is given that, NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Hence, proved.


Question 15:
 If 
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE , show that  NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
It is given that, NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Hence, proved.


Question 16:
 If  
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE, show that NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
The given relationship is NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Taking logarithm on both the sides, we obtain

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Differentiating this relationship with respect to x, we obtain
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Hence, proved.


Question 17:
 If 
NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE, show that NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE


Answer
The given relationship is NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE
Then,

NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE 
Hence, proved.

The document NCERT Solutions Exercise 5.7: Continuity & Differentiability | Mathematics For JEE is a part of the JEE Course Mathematics For JEE.
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