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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 area enclosed between two concentric circles is 770cm 2 . If the radius of the outer circle is 21cm, find the radius of the inner circle. (Ans :14cm) Ans: Π R 2 - Π r 2 =
the probability that an account officer will pass her exam is 5/9. if she pass,the probability that she will be promoted is 3/4. she is not promoted if she fails her professional e
Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia
Solve 9 sin ( 2 x )= -5 cos(2x ) on[-10,0]. Solution At first glance this problem appears to be at odds with the sentence preceding the example. However, it really isn't.
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Equations in linear algebra and matrices What is Equations in linear algebra and matrices?
two fathers and two sons went fishing . they caught only 3 fish and divided them equally among themselves without cutting. is it possible? how?
what is the difference between North America''s part of the total population and Africa''s part
Chain Rule : We've seen many derivatives. However, they have all been functions similar to the following kinds of functions. R ( z ) = √z f (t ) = t 50
Solve 3 + 2 ln ( x /7+3 ) = -4 . Solution This initial step in this problem is to get the logarithm by itself on one side of the equation along with a coefficient of 1.
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