Question

please help me on this question

Answer 1

The length of the set..... \[\cup_{k=1}^{\infty} (X : \frac{ 1 }{ k + 1}\le X \le \frac{ 1 }{ k }\] is

Answer 2

a) 0
b) 1
c) ∞
d) 2

Answer 3

please show your working . very important

Answer 4

ray

Answer 5

and i dont understan tht but i no someone who might

Answer 6

ok. please tag him here

Answer 7

@ganeshie8

Answer 8

@mathmale

Answer 9

@eliassaab or @zzr0ck3r

Answer 10

@zzr0ck3r

Answer 11

@mathmale

Answer 12

@xapproachesinfinity

Answer 13

@mathmale

Answer 14

I'd suggest you actually write out this inequality for several k values, beginning with k=1, k=2, and so on. Doing this myself, I found that X is always clearly delimited by the lower and upper boundaries defined by the value of k.

What is the LONGEST interval within which X might be found, and for which k value does that occur?

Answer 15

yes

Answer 16

i tried k=1, i got 1/2\[\le x \le1\]

Answer 17

when i tried k= 2, i got \[1/3 \le x \le 1/2 \]

Answer 18

and it continued in that pattern but what next should i do?

Answer 19

oh this prob.

Answer 20

mathmale

Answer 21

Again: "What is the LONGEST interval within which X might be found, and for which k value does that occur?"

Answer 22

Let k=2. What are the upper and lower bounds on X?

Answer 23

is it infinity?

Answer 24

No.

The left boundary is 1/(k+1). Let k=2 and calculate this boundary.

Answer 25

yes i have [1/3,1/2]

Answer 26

@mathmale

Answer 27

You have the two boundaries (1/3) and (1/2) when k=2. (1/3) is less than (1/2), so this makes perfect sense.

Now let k have the smallest possible value allowed by the question: 1.

Calculate the lower and upper boundaries, please.

Answer 28

for k=1 , i got [1/2,1]

Answer 29

that is the longest interval you can find that contains X.

Does this answer your question or not?

Answer 30

so, because one is the longest interval generated, the answer is one?

Answer 31

What is 1 - (1/2)? How did you get 1?

Answer 32

1/2 is the answer to 1- (1/2)

Answer 33

So the right option is 1 which is b

Answer 34

Do you have any way in which you could contact your teacher or course administrator?

I asked you to find 1 - (1/2), which comes out to 1/2, so how could the "length" of the set be 1? You may have to clear this up with your teacher.

Answer 35

OK . But is the 1/2 same as its measure?

Answer 36

@mathmale