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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.
Dividing Mixed Numbers Dividing mixed numbers is a 3-step process: 1. Convert the mixed numbers to improper fractions. 2. Divide the fractions 3. Convert the result ba
Find the normalized differential equation which has { x, xe^x } as its fundamental set
HOW MANY number laying between 100 and 1000 can be formed with 0,1,2,3,4,5 and also divisible by 5 with distinct digit
Evaluate following limits. Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our l
PROVE THAT 2 IS IRRATIONAL
Probability Distribution for Continuous Random Variables In a continuous distribution, the variable can take any value within a specified range, e.g. 2.21 or 1.64 compared to
Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative informs you that the
Polynomials in two variables Let's take a look at polynomials in two variables. Polynomials in two variables are algebraic expressions containing terms in the form ax n y m
1. Sketch the Spiral of Archimedes: r= aθ (a>0) ? 2: Sketch the hyperbolic Spiral: rθ = a (a>0) ? 3: Sketch the equiangular spiral: r=ae θ (a>0) ?
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