with proof find the

my guess would be 1 as it is between and by the sandwich rule it convergrs to 1

Results 1 to 15 of 18

- May 26th 2009, 08:02 AM #1

- Joined
- May 2009
- Posts
- 8

- May 26th 2009, 10:05 AM #2

- Joined
- Nov 2008
- Posts
- 461

- May 26th 2009, 10:21 AM #3

- May 26th 2009, 02:43 PM #4

- Joined
- Mar 2009
- Posts
- 256
- Thanks
- 1

- May 26th 2009, 03:51 PM #5

- Joined
- May 2009
- Posts
- 8

- May 26th 2009, 05:55 PM #6

- Joined
- Mar 2009
- Posts
- 256
- Thanks
- 1

- May 26th 2009, 08:06 PM #7

- Joined
- Nov 2006
- From
- Florida
- Posts
- 228

- May 26th 2009, 08:43 PM #8

- Joined
- Nov 2008
- Posts
- 461

- June 13th 2009, 01:19 PM #9

- Joined
- Jun 2009
- Posts
- 220
- Thanks
- 1

Hey, just another slightly different approach without using L'Hopital:

By considering their graphs it's easy to see that

Then the left hand side is easy to calculate:

So on the right hand side

rearraging we arrive at

Using L'Hopital is clearly a lot quicker

Hope this was useful.

- June 13th 2009, 02:45 PM #10

- June 14th 2009, 12:28 AM #11

- June 14th 2009, 01:01 AM #12

- June 14th 2009, 11:45 PM #13

- June 14th 2009, 11:52 PM #14
I like the way you refer to yourself... It would be more interesting to give an outline of the proof... (I've seen some, I'm thinking about anyone who reads this)

That meas that ...

... is continous in because the limit and the value of the function are identical...

- June 15th 2009, 01:30 AM #15
As Dante Alighieri wrote '... perder tempo a chi pił sa pił spiace...', so that the 'proof' I'll give to you is quite elementary...

phase 1: you activate the function 'calculator' in the 'accessories' of Windows...

phase 2: you set the calculator as 'scientific' ...

phase 3 : push in order '0' -> 'x^y' -> '0' -> '='...

After phase 3 in the display of calculator you will read , so that...

Please avoid tedious further discussions ...

Kind regards