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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.
Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
simple predicate
If A be the area of a right triangle and b one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2 Ab /√ b 4 +4A 2 . An
The Mean Value Theorem Assume f(x) is a function that satisfies both of the subsequent. 1. f(x) is continuous on the closed interval [a,b]. 2. f(x) is differentiabl
compare: 643,251: 633,512: 633,893. The answer is 633,512.
find the number of ways 17 employees can b chosen from 327
a tire placed on a balancing machine in a service station starts from rest an d turns through 4.7 revolutions in 1.2 seconds before reaching its final angular speed Calculate its a
how to do multiplication
Sequences Let us start off this section along with a discussion of just what a sequence is. A sequence is nothing much more than a list of numbers written in a particular orde
Patrick gets paid three dollars less than four times what Kevin gets paid. If the number of dollars which Kevin gets paid is represented through x, what does Patrick get paid?
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