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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.
how to find inverse of matrix
log6 X + log6 (x-5) = 1
Q. Give basic Diffrence between Integers and Rational Numbers? Ans. Integers The integers are positive and negative whole numbers. The integers are closed under ad
If z=re i ? ,find the value of |e iz | Solution) z=r(cos1+isin1) |e iz |=|e ir(cos1+isin1) |=|e -rsin1 |=e -rsin1
A standard deck of cards contains 52 cards. One card is selected at random. Determine a) The probability that the card is a 8 or an Ace? b) The probability that the card is
a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950
Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to
The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is
what is the remainder when 75 is divided by 4
Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co
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