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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.
Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6. Ans: No's which are divisible by 6 are
A Pythagorean triple is a set of positive integers (a,b,c) like a2 + b2 = c2. Write a function "ispythag" that will receive 3 positive integers (a, b, c in that order) and will r
which kind of triangle has no congruent sides ?
Multiply following and write the answers in standard form. (a) 7 i ( -5 + 2 i ) (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu
Your friends have opened an ocean fishing operation that requires their fishing vessel to cross a channel, where the depth of the water (measured in metres) varies with time, and i
a²+b²=1 a+b
y'' + 2y = 2 - e-4t, y(0) = 1 use euler''s method with a step size of 0.2 to find and approximate values of y
From the top of a 200 m lighthouse, the angle of depression to a ship in the ocean is 23 . How far is the ship form the base of the lighthouse?
a. Cassie has seven skirts, five blouses, and ten pairs of shoes. How many possible outfits can she wear? b. Cassie decides that four of her skirts should not be worn to school.
an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p
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