The PDE ugy + sin(y) u, = cos(y) Can be reduced to a first order linear equation as: A) uz + cos(x) u =- cos(y) + f(x) B) uz + cos(x) u = y sin(x) + f(x) C) Uy + cos(y) u = - cos(y) + f(y) D) uy + sin(y) u =x cos(y) + /(y) E) None

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Q: 21. Suppose A is a field and suppose also that A closed under countable disjoint unions. Show A

A: This is a question of measure theory.

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Q: All of the following are true for mean EXCEPT *

A: Here use basics of measure

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.