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1. If A and U are two subsets of a normed vector space, and U is open, show that A+U is open. Here A+U={a+u | a belongs to A and u belongs to U}.
2. Suppose {xn} from n=p to infinity is a non-converging subsequence in a compact set of a metric space. Show that it has two convergent subsequences which converge to distinct limit points.
If this problem is too difficult, then perhaps you may solve an easier one, just to give me some direction please. The only example I have is the Riemann function for the telegraph equation
Suppose that a "skew" product of vectors in R2 is defined by (u,v)=u1v1-u2v2. Prove that (u,v)squared >equal too (u,u)(v,v). (NOTE; This is just the reverse of the Cauchy- Schwartz inequality for the ordinary dot product.)
35% of a store's computers come from factory A and the remainder come from factory B.2% of computers from factory A are defective while 1% of computers from factory B are defective.
Let f (x,x',x"). Be a function of independent variables x, its first derivative x', and its second derivative xo. Write down an Euler-Lagrange expression for this function.
A cyclic group is a special kind of group that has many similarities with modular arithmetic.
A manufacturing company produces and sells 20,000 units of a single product. Total products cost are $14 per unit.
Probability of Lamp Failure, A lamp has two bulbs, each of a type with an average lifetime of 6 hours. The probability density function for the lifetime of a bulb
Create an Euler diagram to determine whether the syllogism is valid or invalid: Some nurses are patient.
Small boxes of NutraFlakes cereal arelabeled "net weight 10 ounces." Each hour ,random samples of size n=4 boxes are weighed to check process control. five hours of observations yielded the following:
Chemistry: Delta Systems The element cesium (Cs) freezes at 28.4?, and its molar enthalpy heat of fusion is AHfus=2.09 Kj/mol
What is the "rule of 70"? How long would it take for the price level to double if inflation persisted at (a) 2, (b) 5, and (c) 10 percent per year?
Using trigonometry to solve a Right triangle - Find the width of the lake.
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