Evaluating this limit without Taylor $lim_{xtoinfty} frac{x^3sin(x)}{x^2+x+1}$











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I need help with this limit, and without using Taylor series



$$lim_{xtoinfty} frac{x^3sin(x)}{x^2+x+1}$$










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  • Are you looking for that $frac{x^3sin x}{x^2+x+1}$?
    – gimusi
    Nov 22 at 22:34










  • If it is $displaystylelim_{xtoinfty}frac{x^3sin x}{x^2+x+1}$, then the limit obviously doesn't exist.
    – egreg
    Nov 22 at 22:36















up vote
-2
down vote

favorite












I need help with this limit, and without using Taylor series



$$lim_{xtoinfty} frac{x^3sin(x)}{x^2+x+1}$$










share|cite|improve this question
























  • Are you looking for that $frac{x^3sin x}{x^2+x+1}$?
    – gimusi
    Nov 22 at 22:34










  • If it is $displaystylelim_{xtoinfty}frac{x^3sin x}{x^2+x+1}$, then the limit obviously doesn't exist.
    – egreg
    Nov 22 at 22:36













up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











I need help with this limit, and without using Taylor series



$$lim_{xtoinfty} frac{x^3sin(x)}{x^2+x+1}$$










share|cite|improve this question















I need help with this limit, and without using Taylor series



$$lim_{xtoinfty} frac{x^3sin(x)}{x^2+x+1}$$







limits






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share|cite|improve this question













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edited Nov 22 at 22:41









gimusi

88k74393




88k74393










asked Nov 22 at 22:32









Franco Cabrera

64




64












  • Are you looking for that $frac{x^3sin x}{x^2+x+1}$?
    – gimusi
    Nov 22 at 22:34










  • If it is $displaystylelim_{xtoinfty}frac{x^3sin x}{x^2+x+1}$, then the limit obviously doesn't exist.
    – egreg
    Nov 22 at 22:36


















  • Are you looking for that $frac{x^3sin x}{x^2+x+1}$?
    – gimusi
    Nov 22 at 22:34










  • If it is $displaystylelim_{xtoinfty}frac{x^3sin x}{x^2+x+1}$, then the limit obviously doesn't exist.
    – egreg
    Nov 22 at 22:36
















Are you looking for that $frac{x^3sin x}{x^2+x+1}$?
– gimusi
Nov 22 at 22:34




Are you looking for that $frac{x^3sin x}{x^2+x+1}$?
– gimusi
Nov 22 at 22:34












If it is $displaystylelim_{xtoinfty}frac{x^3sin x}{x^2+x+1}$, then the limit obviously doesn't exist.
– egreg
Nov 22 at 22:36




If it is $displaystylelim_{xtoinfty}frac{x^3sin x}{x^2+x+1}$, then the limit obviously doesn't exist.
– egreg
Nov 22 at 22:36










1 Answer
1






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2
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HINT



Let consider




  • for $x_n=2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to,?$


  • for $x_n=frac{pi}2+2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to ,?$







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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote













    HINT



    Let consider




    • for $x_n=2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to,?$


    • for $x_n=frac{pi}2+2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to ,?$







    share|cite|improve this answer

























      up vote
      2
      down vote













      HINT



      Let consider




      • for $x_n=2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to,?$


      • for $x_n=frac{pi}2+2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to ,?$







      share|cite|improve this answer























        up vote
        2
        down vote










        up vote
        2
        down vote









        HINT



        Let consider




        • for $x_n=2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to,?$


        • for $x_n=frac{pi}2+2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to ,?$







        share|cite|improve this answer












        HINT



        Let consider




        • for $x_n=2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to,?$


        • for $x_n=frac{pi}2+2pi nto infty implies frac{x_n^3sin x_n}{x_n^2+x_n+1}to ,?$








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        answered Nov 22 at 22:37









        gimusi

        88k74393




        88k74393






























             

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