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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

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  1. FoolForMath
    • 3 years ago
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    In order to get the best possible answers, it is helpful if you say in what your thoughts on it are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level.

  2. anjali_pant
    • 3 years ago
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    Well said @FoolForMath ! :p

  3. FoolForMath
    • 3 years ago
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    I know, I am so amazing ;)

  4. anjali_pant
    • 3 years ago
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    Oh please ! WAKE UP ! :P

  5. anjali_pant
    • 3 years ago
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    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
    • 3 years ago
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    who said I need your credence? :P

  7. anjali_pant
    • 3 years ago
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    A FRIEND IN NEED IS A FRIEND INDEED ! So no "faaltu" baatein, help ! :p

  8. FoolForMath
    • 3 years ago
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    Sorry, I don't do baby sitting :P

  9. anjali_pant
    • 3 years ago
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    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
    • 3 years ago
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    Thanks for honouring me with your MEDAL ! :P

  11. anjali_pant
    • 3 years ago
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    Anyways I gtg now , hope to see the answer posted ! :p Cya ! :-)

  12. eliassaab
    • 3 years ago
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    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
    • 3 years ago
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    See for example http://mathworld.wolfram.com/IntegerPart.html

  14. strenesmee
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    [-1.5] = -2. More formally, \[ \lfloor-a \rfloor = - \lceil a \rceil \]

  17. eliassaab
    • 3 years ago
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    You do not have negative numbers now, you have 1 and 1/2

  18. anjali_pant
    • 3 years ago
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    its -1/2

  19. anjali_pant
    • 3 years ago
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    Ok apply LHL to [x] where x->-1/2

  20. eliassaab
    • 3 years ago
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    I did not see the -. I need better glasses.

  21. FoolForMath
    • 3 years ago
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    [ -1/2 ] = [-0.5]=-1

  22. eliassaab
    • 3 years ago
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    [x} is constant at any open interval having end points n, n+1 or n is a positive or negative integer.

  23. eliassaab
    • 3 years ago
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    so -1/2 is in the interval (-1,0). Is {x] continuous at -1/2?

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

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