Reference no: EM131081926
Sample midterm 1 questions-
1. Prove that 1 + √(1+ √2) is irrational.
2. Consider the following series defined for n ∈ N:
∑8n/(n!)2, ∑(-1)n/√(n2 + n).
For each series, determine whether they converge or diverge. If you make use of any of the theorems for determining series properties, you should state which one you use.
3. (a) Let S and T be non-empty bounded subsets of R. Prove that sup S ∪ T = max{sup S, sup T} and sup S ∩ T ≤ min{sup S, sup T}.
(b) Extend part (a) to the cases where S and T are not bounded.
(c) Give an example where sup S ∩ T < min{sup S, sup T}.
4. Suppose that (sn) is a convergent sequence and (tn) is a sequence that diverges to ∞. Prove that limn→∞ sn + tn = ∞.
5. (a) Let (sn) and (tn) be two sequences defined for n ∈ N. Prove that lim sup sn + lim sup tn ≥ lim sup sn + tn.
(b) Construct an example where (lim sup sn) · (lim sup tn) ≠ lim sup(sntn).
6. Let (an) and (bn) are sequences defined for n ∈ N. Suppose that an → a and bn → b as n → ∞ for some a, b ∈ R. If an ≤ bn for all n, show that a ≤ b.
What are e[x|b] and var[x|b]
: What are E[X|B] and Var[X|B]?
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Length of the diameter of the circle
: A circle in thexyxyx, y-plane has the equation (x+92)^2+(y+54)^2=73(x+92)2+(y+54)2=73left parenthes is, x, plus, 92, right parenthesis, start superscript, 2, end superscript
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Perform n bernoulli trials. in each trial
: Perform n Bernoulli trials. In each trial
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Question regarding the quadratic formula
: The solutions are _________ (simplify the answer. Type an exact answer, using radicals and I as needed. Type each solution once . Use a comma to separate answers as needed)
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Determine whether they converge or diverge series
: For each series, determine whether they converge or diverge. If you make use of any of the theorems for determining series properties, you should state which one you use
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What is the probability that the game goes into overtime
: What is the probability that the game goes into overtime?
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Additional columns to the books table
: Add three additional columns to the Books table. The attributes are book ISBN, book secondary desc, and purchase price. Provide SQL statement below.
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List and explain any warning signs that larsen displayed
: Describe any correlations you find in Jendusa-Nicolai's case of victimization and the information in the textbook readings assigned for this module.
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Prepare an annotated webliography on mis issues and trends
: Prepare an annotated webliography on MIS issues, trends, privacy, business practices, Cloud Computing and other aspects of this field. The webliography should include no fewer than 11 and no more than 12 sources.
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