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Problem Questions with Answer, Solution - Exercise 8.5: Linear Approximation and Differential of a function of several variables | 12th Maths : UNIT 8 : Differentials and Partial Derivatives

Chapter: 12th Maths : UNIT 8 : Differentials and Partial Derivatives

Exercise 8.5: Linear Approximation and Differential of a function of several variables

Maths Book back answers and solution for Exercise questions - Mathematics : Differentials and Partial Derivatives: Linear Approximation and Differential of a function of several variables - Exercise Problem Questions with Answer, Solution

EXERCISE 8.5

1. If wxy ) = x3  3xy + 2 y2 , xy  , find the linear approximation for w at (1, 1) .


2. Let z ( xy ) = x2y + 3xy4 , xy  . Find the linear approximation for z at (2, 1) .


3. If v ( xy ) = x2  xy + 1/4 y2 + 7, xy ∈ , find the differential dv .


4. Let V ( xy , z= xy + yz + zxx , yz  . Find the differential dV .


 Let W ( xy,z ) = x2  + 3xy + 3sinz,  xy,z  . Find the linear approximation for z at (2, 1,0) .


Answers:

1. 6x − 7 y − 7

2. – (+ 20 y + 16)

3.  (2x − y dx + (− x + 1/2 y) dy

4. ( y + z)dx + ( x + z)dy + ( y + x)dz

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12th Maths : UNIT 8 : Differentials and Partial Derivatives : Exercise 8.5: Linear Approximation and Differential of a function of several variables | Problem Questions with Answer, Solution

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12th Maths : UNIT 8 : Differentials and Partial Derivatives


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