## DLS 2 years ago limits

1. DLS

$\LARGE \lim_{x \rightarrow 0} \frac{1+e^{\frac{-1}{x}}}{1-e^{\frac{-1}{x}}}$

2. DLS

1) 1 2)-1 3)0 4)Does not exist

3. hartnn

can u use L'Hopitals ?

4. DLS

anything

5. hartnn

then try, x= -1/y to get y->-infinity and then L'Hopitals.

6. DLS

|dw:1358405846397:dw| how will we solve this LHL anyway?

7. hartnn

where did 'a' come from ? did you try x=-1/y ?

8. DLS

its 0 not a nevermind sry :o and i dont want to use L hospital because i know answer is 4 :P

9. hartnn

why do i get -1 ? :P

10. DLS

LHL=-1 RHL=1 Limit does not exist :o

11. hartnn

confirmed with wolf ?

12. DLS

no with answer key..:o but how did we solve LHL to -1

13. hartnn

hmm....you can put h=-h in LHL to get same form as of RHL, that is of h->0+

14. DLS

|dw:1358406440539:dw| but this :/??

15. hartnn

you found RHL ? or not ? because above thing is just substituting x +h=a for that i suggested, x=-1/y instead.(and you get -1 then)

16. DLS

why x=-1/y? can u show clearly :/

17. hartnn

x=-1/y ---->-1/x = y to make the exponent of e as 'y' so that using L'Hopitals is easy (1+e^y)/(1-e^y) -----> e^y/(-e^y) ---->-1

18. DLS

19. hartnn

:P but the limit doesn't exist, right ? you got that using LHL and RHL ?

20. DLS

yes..

21. hartnn

good :)