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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.
A 50-foot pole casts a shadow on the ground. a) Express the angle of elevation θ of the sun as a function of the length s of the shadow. (Hint you may wish to draw this firs
Determine the domain of each of the following functions. f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by
square root 2 on the number line
If the sides angles of a triangle ABC vary in such a way that it''s circum - radius remain constant. Prove that, da/cos A +db/cos B+dc/cos C=0
E1) From your experience, and what you have studied so far, by which age would-you expect an average child to be ready to acquire the following concepts? i) Simple classificatio
UNDETERMINED COEFFICIENTS The way of Undetermined Coefficients for systems is pretty much the same to the second order differential equation case. The simple difference is as t
find the magnitude of the following vectors:5i+7j
Newton's Second Law of motion, which recall from the earlier section that can be written as: m(dv/dt) = F (t,v) Here F(t,v) is the sum of forces which act on the object and m
8
different kind of ellipsoid
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