Show that the limit exists or does not exist

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$lim_(x, y) to (0,0) frac5x^2x^2 + y^2$



let $y = 0$



$lim_x to 0 frac5x^2x^2 = 5$



let $y = x$



$lim_x to 0 frac5x^22x^2 = frac52$



Since different values the limit does not exist.



Would this be right?






multivariable-calculus







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    Possible duplicate of Show that the limit does not exist $lim_(x, y) to (0,0)frac5x^2x^2 + y^2$
    – Nosrati
    55 mins ago














up vote
2
down vote

favorite












$lim_(x, y) to (0,0) frac5x^2x^2 + y^2$



let $y = 0$



$lim_x to 0 frac5x^2x^2 = 5$



let $y = x$



$lim_x to 0 frac5x^22x^2 = frac52$



Since different values the limit does not exist.



Would this be right?






multivariable-calculus







share|cite|improve this question







New contributor




shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.















  • 1




    Possible duplicate of Show that the limit does not exist $lim_(x, y) to (0,0)frac5x^2x^2 + y^2$
    – Nosrati
    55 mins ago












up vote
2
down vote

favorite









up vote
2
down vote

favorite











$lim_(x, y) to (0,0) frac5x^2x^2 + y^2$



let $y = 0$



$lim_x to 0 frac5x^2x^2 = 5$



let $y = x$



$lim_x to 0 frac5x^22x^2 = frac52$



Since different values the limit does not exist.



Would this be right?






multivariable-calculus







share|cite|improve this question







New contributor




shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











$lim_(x, y) to (0,0) frac5x^2x^2 + y^2$



let $y = 0$



$lim_x to 0 frac5x^2x^2 = 5$



let $y = x$



$lim_x to 0 frac5x^22x^2 = frac52$



Since different values the limit does not exist.



Would this be right?






multivariable-calculus




multivariable-calculus






share|cite|improve this question







New contributor




shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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shah is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 1




    Possible duplicate of Show that the limit does not exist $lim_(x, y) to (0,0)frac5x^2x^2 + y^2$
    – Nosrati
    55 mins ago












  • 1




    Possible duplicate of Show that the limit does not exist $lim_(x, y) to (0,0)frac5x^2x^2 + y^2$
    – Nosrati
    55 mins ago







1




1




Possible duplicate of Show that the limit does not exist $lim_(x, y) to (0,0)frac5x^2x^2 + y^2$
– Nosrati
55 mins ago




Possible duplicate of Show that the limit does not exist $lim_(x, y) to (0,0)frac5x^2x^2 + y^2$
– Nosrati
55 mins ago










2 Answers
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Yes that's right, more in general we can see that by $y=mx$



$$frac5x^2x^2 + y^2=frac51+m^2$$



or by polar coordinates



$$frac5x^2x^2 + y^2=5cos^2theta$$



which depend respectively upon $m$ and $theta$.



You can find many others similar questions on MSE, as for example



  • Calculate the limit given.

  • Limit with two-variable function





share|cite|improve this answer





























    up vote
    1
    down vote













    That’s right: if the limit exists, all the restriction of the function have the same limit. This is not the case, hence the limit does not exist.






    share|cite|improve this answer




















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      2 Answers
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      2 Answers
      2






      active

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      active

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      up vote
      2
      down vote













      Yes that's right, more in general we can see that by $y=mx$



      $$frac5x^2x^2 + y^2=frac51+m^2$$



      or by polar coordinates



      $$frac5x^2x^2 + y^2=5cos^2theta$$



      which depend respectively upon $m$ and $theta$.



      You can find many others similar questions on MSE, as for example



      • Calculate the limit given.

      • Limit with two-variable function





      share|cite|improve this answer


























        up vote
        2
        down vote













        Yes that's right, more in general we can see that by $y=mx$



        $$frac5x^2x^2 + y^2=frac51+m^2$$



        or by polar coordinates



        $$frac5x^2x^2 + y^2=5cos^2theta$$



        which depend respectively upon $m$ and $theta$.



        You can find many others similar questions on MSE, as for example



        • Calculate the limit given.

        • Limit with two-variable function





        share|cite|improve this answer
























          up vote
          2
          down vote










          up vote
          2
          down vote









          Yes that's right, more in general we can see that by $y=mx$



          $$frac5x^2x^2 + y^2=frac51+m^2$$



          or by polar coordinates



          $$frac5x^2x^2 + y^2=5cos^2theta$$



          which depend respectively upon $m$ and $theta$.



          You can find many others similar questions on MSE, as for example



          • Calculate the limit given.

          • Limit with two-variable function





          share|cite|improve this answer














          Yes that's right, more in general we can see that by $y=mx$



          $$frac5x^2x^2 + y^2=frac51+m^2$$



          or by polar coordinates



          $$frac5x^2x^2 + y^2=5cos^2theta$$



          which depend respectively upon $m$ and $theta$.



          You can find many others similar questions on MSE, as for example



          • Calculate the limit given.

          • Limit with two-variable function






          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 48 mins ago

























          answered 54 mins ago









          gimusi

          80k73990




          80k73990




















              up vote
              1
              down vote













              That’s right: if the limit exists, all the restriction of the function have the same limit. This is not the case, hence the limit does not exist.






              share|cite|improve this answer
























                up vote
                1
                down vote













                That’s right: if the limit exists, all the restriction of the function have the same limit. This is not the case, hence the limit does not exist.






                share|cite|improve this answer






















                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  That’s right: if the limit exists, all the restriction of the function have the same limit. This is not the case, hence the limit does not exist.






                  share|cite|improve this answer












                  That’s right: if the limit exists, all the restriction of the function have the same limit. This is not the case, hence the limit does not exist.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 2 hours ago









                  Blumer

                  35619




                  35619




















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