NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

The document NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Continuity & Differentiability

 Question 1:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRevNCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Question 2:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev         NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 3:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 4:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Answer
The given relationship is NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Differentiating this relationship with respect to x, we obtain

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 5: 

Find NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Answer

The given relationship is x2 +xy +y2 = 100

Differentiating this relationship with respect to x, we obtain 

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

[Derivative of constant function is 0] 

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 6:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 7:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Using chain rule, we obtain
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 8:

Find NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
The given relationship is

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Differentiating this relationship with respect to x, we obtain
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 9:

Find  NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Therefore, by quotient rule, we obtain

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 10:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev  NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
 

Question 11:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev  NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Answer
The given relationship is,

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

On comparing L.H.S. and R.H.S. of the above relationship, we obtain  tany/2 = x

Differentiating this relationship with respect to x, we obtain 

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 12:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev  NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
The given relationship is NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

 

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
From (1), (2), and (3), we obtain

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Differentiating this relationship with respect to x, we obtain

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 13:

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Question 14:

Find NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
Differentiating this relationship with respect to x, we obtain

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev
 


Question 15:

Find dy/dx  NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev


Answer
NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

Differentiating this relationship with respect to x, we obtain 

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

NCERT Solutions - Continuity & Differentiability, Exercise 5.3Maths JEE Notes | EduRev

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