## anonymous 3 years ago Evaluate the limit:

1. anonymous

|dw:1355798329824:dw|

2. anonymous

I got to the point where I transformed it to: |dw:1355798387822:dw|

3. Zarkon

$\lim_{x\to\infty}\left(1+\frac{a}{x}\right)^{bx}=e^{ab}$

4. anonymous

Well... I would like to use L'hospital's rule...

5. Zarkon

then use it :)

6. anonymous

I can't :( . I am stuck.

7. Zarkon

differentiate the top and the bottom...what is the holdup

8. anonymous

|dw:1355798464643:dw|

9. anonymous

The problem is if I keep using L'hospital's rule it's not really going to help...

10. anonymous

I still keep getting 0/0 .

11. Zarkon

why do you have a 4

12. anonymous

Isn't the derivative of 1/(2x) -1/(4x^2) ?

13. Zarkon

no

14. anonymous

That could be my mistake.

15. Zarkon

$\frac{d}{dx}\frac{1}{2x}=\frac{-1}{2x^2}$

16. anonymous

Right... :P .

17. Zarkon

you should be able to cancel out the $$x^2$$'s

18. Zarkon

|dw:1355798716195:dw|

19. Zarkon

|dw:1355798750796:dw|

20. anonymous

Thanks :) . I did a lot more work but got it :) .

21. Zarkon

good