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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.
I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?
Evaluate following limits. Solution Let's begin with the right-hand limit. For this limit we have, x > 4 ⇒ 4 - x 3 = 0 also, 4 - x → 0 as x → 4
if an object weighed 11 pounds how many ounces would it weigh
Solve the equation for exact solutions over the interval [o,2Pi] 2 sec x + 1 = sec x + 3 Some one please help!!!
how long would it take if a submarine if it goes 3 feet per minute to get to 20000 answer
The following table given the these scores and sales be nine salesman during last one year in a certain firm: text scores sales (in 000''rupees) 14 31 19
A circle is inscribed in a triangle ABC having sides 8cm, 10cm and 12cm as shown in the figure. Find AD, BE and CF.
Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero. So, let ε 0 so that the following will be true. |x 2 - 0|
Write a function that computes the product of two matrices, one of size m × n, and the other of size n × p. Test your function in a program that passes the following two matrices t
A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruits are there?
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