Theoretical Concepts of Calculus

angelet

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Find the interior int (S), the boundary bd (S), the closure cl (S), and the set accumulation points S' of each subset S of R.
Classify the set S as open, closed, neither, or both. Is S a compact set? Justify your answers.


For each subset S of R, fi…nd its supremum sup S, maximum max S, infi…mum inf S, and minimum min S, if exists. Otherwise, write "DNE". Justify your answers.

a. S = { (-1)^n + (-1)^n/n | n is an element of N }


b. S = U [ -2+1/(n^2), 2-1(2n+1) ] when n is an element of N


c. S = nQ \ {pi}


d. S = { x is an element of R | 0 < x^2 <= 3 }



please answer any of the following questions, if not all.
 
media%2Fab6%2Fab6f9b60-38e0-41f8-a6eb-4b24c057c186%2FphpB9vrVh.png

media%2F0d2%2F0d276417-b2fb-46e6-9e04-158dfd765d2d%2FphpcnUUXU.png

Find the interior int (S), the boundary bd (S), the closure cl (S), and the set accumulation points S' of each subset S of R.
Classify the set S as open, closed, neither, or both. Is S a compact set? Justify your answers.


For each subset S of R, fi…nd its supremum sup S, maximum max S, infi…mum inf S, and minimum min S, if exists. Otherwise, write "DNE". Justify your answers.

a. S = { (-1)^n + (-1)^n/n | n is an element of N }


b. S = U [ -2+1/(n^2), 2-1(2n+1) ] when n is an element of N


c. S = nQ \ {pi}


d. S = { x is an element of R | 0 < x^2 <= 3 }



please answer any of the following questions, if not all.

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")
 
Have you calculated what numbers are in each of these sets?
For example, for \(\displaystyle \{(-1)^n+ \frac{(-1)^n}{n}| n\in N\}\)
we have, for n= 1, -1- 1= -2; for n= 2; 1+ 1/2= 3/2; for n= 3, -1- 1/3= -4/3; for n= 4, 1+ 1/4= 5/4; for n= 5, -1- 1/5= -6/5; for n= 6, 1+ 1/6= 7/6, etc. Those are the numbers in the set.

For \(\displaystyle \cup_{n\in N} \left(-2+ \frac{1}{n^2}, 2- \frac{1}{2n+1}\right)\)
for n= 1, (-2+ 1, 2- 1/3)= (-1, 5/3); for n= 2, (-2+ 1/4, 2- 1/5)= (-7/4, 9/5); for n= 3, (-2+ 1/9, 2- 1/7)= (-17/9, 13/7),etc Take the intersections of those.


I have no clue what "\(\displaystyle nQ\ \{\pi\}\)" means! Q is the set of rational numbers but what is nQ? And \(\displaystyle \pi\) is not in Q so how can you remove it?

\(\displaystyle \{ x\in R| 0< x^2\le 3\}\) is just all numbers larger than of equal to \(\displaystyle \sqrt{3}\) and less than 0 together with all numbers larger than 0 and less than or equal to \(\displaystyle \sqrt{3}\): \(\displaystyle \left[\sqrt{3}, 0\right)\cup \left(0, \sqrt{3}\right]\).
 
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