lim ((1/sqrtx)-1)/(x-1)

x>1

(1-sqrtx/sqrtx)/(x-1)

why does this end up looking like this (1-sqrtx)/(sqrtx(x-1))

i am having a brain fart need this for my exam :D

Printable View

- Apr 20th 2006, 11:57 AMtnkfublimit - more about division
lim ((1/sqrtx)-1)/(x-1)

x>1

(1-sqrtx/sqrtx)/(x-1)

why does this end up looking like this (1-sqrtx)/(sqrtx(x-1))

i am having a brain fart need this for my exam :D - Apr 20th 2006, 01:21 PMJameson

As you said, this is equivalent to

Now would be a good time to use L'Hopital's rule, if you have learned this. Have you? - Apr 21st 2006, 08:59 PMearbothQuote:

Originally Posted by**tnkfub**

here is a way to solve this problem without using the l'Hospital rule:

Substitute the x by (1+1/n) and calculate the limit for n approaching infinity:

After a few steps of very unpleasant transformation you'll get:

Greetings

EB - Apr 22nd 2006, 05:04 PMThePerfectHackerQuote:

Originally Posted by**tnkfub**

You can express as,

Thus,

Thus,

Thus,

Thus,

As, you have,

- Apr 22nd 2006, 05:24 PMThePerfectHackerQuote:

Originally Posted by**earboth**

*prove*that such a substitution is valid?

Not that I am arguing I am simply interested. - Apr 22nd 2006, 10:37 PMearbothQuote:

Originally Posted by**ThePerfectHacker**

honestly speaking: No.

1. When you calculate the derivative you calculate for instance the limit

2. I made an analoguous conclusion to use this method with this problem. I noticed that it worked fine. But of course that isn't a proof.

Greetings

EB - Apr 23rd 2006, 06:30 AMThePerfectHackerQuote:

Originally Posted by**earboth**