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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 an example for each of the following, or explain why no example exists. (a) A non-diagonalisable (square) matrix. (b) A square matrix (having real entries) with no real eigenvalues. (c) A 2 x 2 matrix B such that B3 = A where A = (d) A diagonalisable matrix A such that A2 is not diagonalisable.