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1.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even. 2.Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2. 3.let r>0 and S={x in R^3:(x1)^2+(x2)^2+(x3)^2<(r)^2} show that diam S=2r.4.let x=(x1,...xn) in Rn.show that (? k=1,n xk)^2<=n|x|^2.
definition and examples and types
One integer is four times other. The sum of the integers is 5. What is the value of the lesser integer? Let x = the lesser integer and now let y = the greater integer. The ?rst
Higher-Order Derivatives It can be seen that the derivative of a function is also a function. Considering f'x as a function of x, we can take the derivative
The time has at last come to describe "nice enough". We've been using this term during the last few sections to explain those solutions which could be used to form a general soluti
show that all primes except 2, are of the form 4n-1 or 4n+1.
To begin with we have counting numbers. These numbers are also known as natural numbers and are denoted by a symbol 'N'. These numbers are obtai
How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren
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Compute the dot product for each of the subsequent equation (a) v → = 5i → - 8j → , w → = i → + 2j → (b) a → = (0, 3, -7) , b → = (2, 3,1) Solution (a) v →
With your current loan, explain how much additional money you would need to add to your monthly payment to pay off your loan in 20 years instead of 25. Decide whether or not it wou
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