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Problem 3. Prove or give a counter example 1. If an converges to a real limit then limn700 (m)" = 0. 2. If an is a positive sequence satisfying limn+ ()" = 0 then it con- verges.
1 a). Give a counter example to the proposition: Every positive integer which ends in 31 is a prime. b). Give a proof by cases that min{s, t} + max{s, t} = s + t for any real numbers s and t. Hint: One of the cases you might use is s ≤ t or s < t. Depending on your choice, what would be the other case(s)? c). Give an indirect proof that if 2n 3 + 3n +...
Write an example of a proof by contradiction . ( any proof dealing with real/math analysis)
Real Analysis
2.3 Give an example of a mapping which is neither injective nor surjective.
Please use same format for counter example
This is an invalid argument, make a counter example 12.5 | Vy [Cube(y) V Dodec(y)] 1x [Cube(x) + Large(x)] 3x Large(x) 3x [Dodec(x) A Small(x)]
Give an example of a set S and a sequence (xn) that is frequently in S and a partial limit of x of (xn) such that x fails to be close to S. (Real Analysis)
Search the web to find one real-life example of a situation where a government has/had imposed price floor/ceiling. Write your analysis on the outcome of this policy.
Explain the concept of value of perfect information in decision analysis. Give a real world example where the value of perfect information will be useful to a decision maker
Discuss each of the steps in the quantitative analysis approach using a business example. Be sure to use terms and concepts from your reading this week in your post. Also, make sure to develop a real mathematical model of the situation. Sources must be cited for credit. Read the rubric and requirements for full credit below.
Give a real world example of a derivative project, a platform project using an example of a real product marketed by a real firm.