EXERCISE . . In each of the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree.
(i) f x y x y ( , ) = (ii) h x y x y x y ( , ) = (iii) g x y z z ( , , ) = (iv) U x y z z ( , , ) . Prove that f x y x y ( , ) = is homogeneous; what is the degree? Verify Euler’s Theorem for f . .
Prove that g x y is homogeneous; what is the degree? Verify Euler’s Theorem for g . . If u x y ( , ) = , prove that x u y u ∂ + = .
If v x y , prove that x v y v ∂ + ∂ = . . If w x y z x y y xz y z ( , , ) , find x w y w z w z and - - Differentials and Partial Derivatives EXERCISE . Choose the correct or the most suitable answer from the given four alternatives : .
A circular template has a radius of cm. The measurement of radius has an approximate error of . cm. Then the percentage error in calculating area of this template is ( ) .
The percentage error of fifth root of is approximately how many times the percentage error in ? ( ) ( ) ( ) ( ) . If u x y e x ( , ) = , then ∂ x is equal to ( ) e x ( ) xu ( ) x u ( ) y u . If v x y log( , then ∂ ∂ + ∂ v v y is equal to ( ) e ( ) ( ) ( ) .
If w x y > , then ∂ w x is equal to ( ) x y