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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.
(a+b+c)2=
Given that 2t 2 y′′ + ty′ - 3 y = 0 Show that this given solution are form a fundamental set of solutions for the differential equation? Solution The two solutions f
Consider the function f: N → N, where N is the set of natural numbers, defined by f(n) = n 2 +n+1. Show that the function f is one-one but not onto. Ans: To prove that f is one
Speaking Mathematically : A Class 2 teacher was explaining the concept of place value to his students, using the number eleven. He started by saying "One and one make eleven." So
Find the magnitude of the following vectors: 5i+7j
Change of base: The final topic that we have to look at in this section is the change of base formula for logarithms. The change of base formula is,
The equation -2x^2-kx-2=0 has two different real soultions. find the set of possible values for k.
Here we learn: 1) Discussed what counting means, and stressed that it is not the ability to recite number names. 2) Talked about the need for a child to understand several pr
Q. Adding Fractions with the Same Denominator? Adding fractions with the same denominator is easy- you add the numerators (the tops), and you leave the denominator alone!
A graph with a positive slope shows that the variables depicted on the axes goes in the similar directions.
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