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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.
Evaluate the below given limit. Solution Note as well that we actually do have to do the right-hand limit here. We know that the natural logarithm is just described fo
Adding Equally Sized Groups: Once children have had enough practice of making groups of equal size, you can ask them to add some of these equal groups. They can now begin to atte
How far will a bowling ball goes in one rotation if the ball has a diameter of 10 inches? (π = 3.14) 1. 78.5 in 2. 31.4 in 3. 62.8 in 4. 15.7 in 2. The circumfere
(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co
the low temperature in onw city was -4degrees Fahrenheit. The low temperature in another city was 8degrees Fahrenheit. what is an inequality to compare those temperatures
Design an automaton that accepts just only even numbers of 0s and even number of 1's. Ans: The needed automata that accepts even number of 0's and even number of 1's is specifi
Chain Rule : We've seen many derivatives. However, they have all been functions similar to the following kinds of functions. R ( z ) = √z f (t ) = t 50
If 0.3 is added to 0.2 times the quantity x - 3, the result is 2.5. What is the value of x? The statement, "If 0.3 is added to 0.2 times the quantity x - 3, the result is 2.5,
Derivative with Polar Coordinates dy/dx = (dr/dθ (sin θ) + r cos θ) / (dr/dθ (cosθ) - r sinθ) Note: Rather than trying to keep in mind this formula it would possibly be easi
E1) Do you agree that multiplication and division should be learnt intermeshed with each other, or not? Give reasons for your answer. E2) How would you explain to children wh
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