InterviewSolution
Saved Bookmarks
| 1. |
Which one of the following function(s) is/are homogeneous? |
|
Answer» `f(X,y) = (x-y)/(x^(2)+y^(2))` THUS, it is homogenous of degree `-1` b) `f(lambdax,lambday)=(lambdax)^(1//3)(lambday)^(-2//3)tan^(-1)x/y` `=lambda^(-1//3)x^(1//3)tan^(-1)x/y` `=lambda^(-1//3)f(x,y)` C) `f(lambdax,lambday) = lambdax("ln"sqrt(lambda^(2)(x^(2)+y^(2))-"ln "lambday))+lambdaye^(x//y)` `=lambdax["ln"((lambdasqrt(x^(2)+y^(2)))/(lambday))]+lambdaye^(x//y)` `lambda[x("ln "sqrt(x^(2)+y^(2))-"ln"y)+ye^(x//y)]` `=lambdaf(x,y)` Thus, it is homogeneous. d) `f(lambdax,lambday)=lambdax["ln "(2lambda^(2)x^(2)+lambda^(2)y^(2))(lambdaxlambda(x+y))]+lambda^(2)x^(2)tan(x+2y)/(3x-y)` `=lambda x["ln "(2x^(2)+y^(2))/(x(x+y))]+lambda^(2)x^(2)tan(x+2y)/(3x-y)` Thus, it is non-homogeneous. |
|