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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 ships are sailing in the sea on either side of a lighthouse; the angles of depression of two ships as observed from the top of the lighthouse are 600 and 450 re
Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C. Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0
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
y=2x+3=
The Shape of a Graph, Part II : In previous we saw how we could use the first derivative of a function to obtain some information regarding the graph of a function. In this secti
Arc Length with Parametric Equations In the earlier sections we have looked at a couple of Calculus I topics in terms of parametric equations. We now require to look at a para
Find the volume of a right circular cylinder: Calculate the volume and surface area of a right circular cylinder along with r = 3" and h = 4". Solution: V = πr 2
how to do multiplication
To help Himalya herbal launch a successful marketing campaign in the UK
Now we have to look at rational expressions. A rational expression is a fraction wherein the numerator and/or the denominator are polynomials. Here are some examples of rational e
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