using the Epsilon-N definition of the limit prove this !

1 answer below »
using the Epsilon-N definition of the limit prove this !

Answered Same DayDec 20, 2021

Answer To: using the Epsilon-N definition of the limit prove this !

Robert answered on Dec 20 2021
120 Votes
So let � > 0. We have to show that ∣∣∣∣n · (√n2 + 2− n)− 1∣∣∣∣ <�∣∣∣∣ 2n√n2 + 2+ n − 1
∣∣∣∣ < �∣∣∣∣
n−

n2 + 2
n+

n2 + 2
∣∣∣∣ < �
1−

1+ 2n2
1+

1+ 2n2
∣∣∣∣ < �
Now for n > n0 we have
∣∣ 2
n2
∣∣ < �. Let t0 = √1+ �. Therefore we have
1− t0
1+ t0
which is an arbitrary...
SOLUTION.PDF

Answer To This Question Is Available To Download

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here