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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.
The first particular case of first order differential equations which we will seem is the linear first order differential equation. In this section, unlike many of the first order
A recipe calls for 2 1/4 teaspoons of salt for every 1 1/8 teaspoons of black pepper used. How many teaspoons of salt are needed for each teaspoon of pepper used ?
A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =
Eliminate the parameter from the subsequent set of parametric equations. X = t 2 + t Y = 2t - 1 Solution: One of the very easy ways to eliminate the parameter is to
Whlie solving complex number 1pi in polar form.In book they have taken theta =-pi/4 why not 7pi/4 because the point lie in fourth quadrant and the theta is given by 2pi-angle(alpha
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If 7sin 2 ?+3cos 2 ? = 4, show that tan? = 1/√3 . Ans: If 7 Sin 2 ? + 3 Cos 2 ? = 4 S.T. Tan? 1/√3 7 Sin 2 ? + 3 Cos 2 ? = 4 (Sin 2 ? + Cos 2 ?)
Determine if the following series converges or diverges by using limit comparison test. Solution To make use of the limit comparison test we require to find out a seco
Conditional Probability: Independent Events If the probability of an event is subject to a restriction on the sample space, the probability is said to be conditional. Co
x ?8x ?16x ? 0, x?0? ? 0, x?0? ? 2
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