Question

Please, help
show that lim (2n/(n+2) ) =2

Answer 1

Let \(\varepsilon\) >0, calculate N
\[|\dfrac{2n}{n+2}| -2= |\dfrac{-4}{n+2}|=\varepsilon\]
since lim of the sequence implies that n goes to infinitive, so that, we just take the positive value
\[\dfrac{-4}{n+2}= \varepsilon\] which gives me n = \(\dfrac{-4}{\varepsilon} -2\)
and let N = \(\dfrac{-4}{\varepsilon} -2\)
then \(\forall n >N\) \(\dfrac{-4}{n+2}<\dfrac{-4}{N+2}\)

Answer 2

and I stuck here.

Answer 3

Do I make mistake at absolute value of -4/ n +2??
should it be \(|\dfrac{-4}{n+2}|= \dfrac{4}{n+2}\)??
since n>0 --> the absolute value must take >0 value of (-4) , right?
@kirbykirby I saw you stop by my post. Thanks in advance, :)

Answer 4

Are you doing an epsilon-delta proof for a limit?

Answer 5

Yes,

Answer 6

On lecture note, my prof said that we calculate N on the draft paper by solving for n from \((a_n - L)=\varepsilon\)

Answer 7

oye.. I'm not sure if I'll be of much help. I somehow managed to skip epsilon-delta proofs in my calculus courses :o So.. I never really much much practice with these :(

Answer 8

then plug back on the main proof the value of N

Answer 9

:( for this course (advance calculus), we must know how to prove calculus problems, not problems themselves. That's why I have to go into detail like this.

Answer 10

Hm yes. Ya I somehow managed to skip it since I changed schools from cal 1 to cal 2, and my cal 1 wasn't very proof based.. Anyway, good luck , sorry :(

Answer 11

hihihi.. not worry , it is just homework, and my prof is cool. If I ask, he will answer. :)

Answer 12

:)

Answer 13

I gooooooooooooooot it, hihii

Answer 14

yay