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Give an example of each of the following given below . You do not require to give any justi cation.
(a) A nonempty, bounded subset of Q with no in mum in Q.
(b) A subspace of R containing N in which {1} is open but (2) is not.
(c) A nonempty subspace of Q which is complete in the metric space sense.
(d) An uncountable open subset of R\Q which is not all of R\Q.
(e) A bounded sequence in {x € R\Q } - 1 < x < 1} which is not Cauchy in R.
Evaluate following limits. Solution Let's begin with the right-hand limit. For this limit we have, x > 4 ⇒ 4 - x 3 = 0 also, 4 - x → 0 as x → 4
Definition 1. Given any x 1 & x 2 from an interval I with x 1 2 if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2. Given any x 1 & x 2 from an interval
Are the two angles of a rectangles congruent ? why ?
The sum of two numbers is 19, their difference is 5. find the numbers
Find the normalized differential equation which has {x, xex} as its fundamental set
scope of operation research and its limitations
how to see shares and dividends of a company and are they seen day wise?
Solve 6 sin ( x/2)= 1 on [-20,30] Solution Let's first work out calculator of the way since that isn't where the difference comes into play. sin( x/2)= 1/6 ⇒x/2= sin
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation. Carrying out
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