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Calculus (MindTap Course List)
- [Type here] 21. Prove that ifand are integral domains, then the direct sum is not an integral domain. [Type here]arrow_forwardFor an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.arrow_forward5. Prove that the equation has no solution in an ordered integral domain.arrow_forward
- Prove that if a subring R of an integral domain D contains the unity element of D, then R is an integral domain. [Type here][Type here]arrow_forwardIf x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xyarrow_forwardIf a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?arrow_forward
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