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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.
Two people on bikes are at a distance of 350 meters. Person A begin riding north at a rate of 5 m/sec and 7 minutes later on Person B begin riding south at 3 m/sec. Determine th
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Factoring polynomials Factoring polynomials is done in pretty much the similar manner. We determine all of the terms which were multiplied together to obtain the given polynom
Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second
State the following statement as a disjunction (in DNF) as well using quantifiers: There does not exit a woman who has taken a flight on each airline in the world.
Q. Define Combined Functions? Ans. We are often interested in functions which combine a trigonometric function with another type of function. For example, y = x + sinx wi
Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To beg
Example of Rounding Off: Example: Round off the subsequent number to two decimal places. 6.238 Solution: Step 1: 8 is the number to the right of t
a wheel revolves 360 deegre revolution in one minute .Find how many radians will the wheel subtend in one second
Negative function : Several functions are not positive however. Consider the case of f (x ) =x 2 - 4 on [0,2]. If we utilizes n = 8 and the midpoints for the rectangle height w
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