## anjali_pant 3 years ago CONTINUITY QUESTION : Examine the continuity of the function : f(x)= ( 2[x] )/ ( 3x-|x| ) at x=-1/2 and x=1

1. FoolForMath

2. anjali_pant

Well said @FoolForMath ! :p

3. FoolForMath

I know, I am so amazing ;)

4. anjali_pant

Oh please ! WAKE UP ! :P

5. anjali_pant

Anyways , I will believe that you are SUPER-DUPER AMAZING , only when you will SOLVE THIS question ! :p And please no direct answers , the whole explanation is required :p

6. FoolForMath

who said I need your credence? :P

7. anjali_pant

A FRIEND IN NEED IS A FRIEND INDEED ! So no "faaltu" baatein, help ! :p

8. FoolForMath

Sorry, I don't do baby sitting :P

9. anjali_pant

Now from where on this earth "baby sitting" came ? Iam asking you to help me solve an ECO(H) , 2nd year maths question , not to sing a lullaby ! :p Had hai matlab ! ;p

10. anjali_pant

Thanks for honouring me with your MEDAL ! :P

11. anjali_pant

Anyways I gtg now , hope to see the answer posted ! :p Cya ! :-)

12. eliassaab

You should not worr y about the denominator. It is continious at any x except at x=0. All you have to examine is the function g(x) = [x]. Where is the function g(x) discontinuous?

13. eliassaab

See for example http://mathworld.wolfram.com/IntegerPart.html

14. strenesmee

check right and left limits at x=-1/2 and x=1 If right limits are equal to left limits the function is continuous

15. anjali_pant

Iam not able to deal with [x] ! :-( When there is a positive number inside [x] , that's ok with me , but when there is a negative number , Iam not able to apply the left/right hand limit ! Please help

16. FoolForMath

[-1.5] = -2. More formally, \[ \lfloor-a \rfloor = - \lceil a \rceil \]

17. eliassaab

You do not have negative numbers now, you have 1 and 1/2

18. anjali_pant

its -1/2

19. anjali_pant

Ok apply LHL to [x] where x->-1/2

20. eliassaab

I did not see the -. I need better glasses.

21. FoolForMath

[ -1/2 ] = [-0.5]=-1

22. eliassaab

[x} is constant at any open interval having end points n, n+1 or n is a positive or negative integer.

23. eliassaab

so -1/2 is in the interval (-1,0). Is {x] continuous at -1/2?

24. anjali_pant

Heya ! Iam finally through with this question. So before closing this question , I would like to thank all of you-" THANK YOU !" :-)