# limit of ((x(sqrt(x+2)))/sqrt(x+1))-x is 1/2? Why?

### #1

Posted 28 July 2016 - 08:17 PM

### #2

Posted 28 July 2016 - 09:30 PM

Limit = 1/2, since the denominator ->2x.

### #3

Posted 28 September 2016 - 03:49 AM

You should use l'Hôpital's rule for a rigorous proof:

(see the previous post).

Using l'Hôpital's rule, this equals . Assuming the limit exists, this is equal to .

You then evaluate : Using l'Hôpital again, this is equal to . It follows that this limit is 1, and therefore .

**Edited by renerpho, 28 September 2016 - 03:52 AM.**

### #4

Posted 31 December 2016 - 02:25 AM

Why use L'Hopital's rule? Mathematic's answer is much simpler.

### #5

Posted 31 December 2016 - 03:58 PM

[14:02] <Sato> want

[14:02] <Sato> Schroedinger

[14:04] == Schroedingers_hat [~matt@CPE-121-222-209-157.lnse1.woo.bigpond.net.au] has joined #sfn

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