Determining $lim_{(x, y) to (2y, y)} exp(frac{|x-2y|}{(x-2y)^2})$












3














Find the limit of $$expleft(frac{|x-2y|}{(x-2y)^2}right)$$ when $(x,y) to (2y,y)$.



I have considered two cases: $(x-2y)<0 $ and $(x-2y)>0$.
But in first case the limit turns out to be $0$ and in the second case limit is undefined. I am not sure if my solution is correct or not.










share|cite|improve this question




















  • 1




    hint $(x-2y)^2=|x-2y|^2$
    – dmtri
    Dec 15 at 8:36






  • 1




    $e^{frac{1}{0}}=infty$ if we go frrom the right of $0$
    – dmtri
    Dec 15 at 8:39
















3














Find the limit of $$expleft(frac{|x-2y|}{(x-2y)^2}right)$$ when $(x,y) to (2y,y)$.



I have considered two cases: $(x-2y)<0 $ and $(x-2y)>0$.
But in first case the limit turns out to be $0$ and in the second case limit is undefined. I am not sure if my solution is correct or not.










share|cite|improve this question




















  • 1




    hint $(x-2y)^2=|x-2y|^2$
    – dmtri
    Dec 15 at 8:36






  • 1




    $e^{frac{1}{0}}=infty$ if we go frrom the right of $0$
    – dmtri
    Dec 15 at 8:39














3












3








3


1





Find the limit of $$expleft(frac{|x-2y|}{(x-2y)^2}right)$$ when $(x,y) to (2y,y)$.



I have considered two cases: $(x-2y)<0 $ and $(x-2y)>0$.
But in first case the limit turns out to be $0$ and in the second case limit is undefined. I am not sure if my solution is correct or not.










share|cite|improve this question















Find the limit of $$expleft(frac{|x-2y|}{(x-2y)^2}right)$$ when $(x,y) to (2y,y)$.



I have considered two cases: $(x-2y)<0 $ and $(x-2y)>0$.
But in first case the limit turns out to be $0$ and in the second case limit is undefined. I am not sure if my solution is correct or not.







calculus






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 15 at 14:27









amWhy

191k28224439




191k28224439










asked Dec 15 at 8:24









Kashmira

463




463








  • 1




    hint $(x-2y)^2=|x-2y|^2$
    – dmtri
    Dec 15 at 8:36






  • 1




    $e^{frac{1}{0}}=infty$ if we go frrom the right of $0$
    – dmtri
    Dec 15 at 8:39














  • 1




    hint $(x-2y)^2=|x-2y|^2$
    – dmtri
    Dec 15 at 8:36






  • 1




    $e^{frac{1}{0}}=infty$ if we go frrom the right of $0$
    – dmtri
    Dec 15 at 8:39








1




1




hint $(x-2y)^2=|x-2y|^2$
– dmtri
Dec 15 at 8:36




hint $(x-2y)^2=|x-2y|^2$
– dmtri
Dec 15 at 8:36




1




1




$e^{frac{1}{0}}=infty$ if we go frrom the right of $0$
– dmtri
Dec 15 at 8:39




$e^{frac{1}{0}}=infty$ if we go frrom the right of $0$
– dmtri
Dec 15 at 8:39










2 Answers
2






active

oldest

votes


















5














It is :



$$lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{(x-2y)^2}}right) = lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{|x-2y|^2}}right)$$
$$=$$
$$lim_{(x,y) to (2y,y)} expleft({frac{1}{|x-2y|}}right) equiv lim_{z to 0} expleft(frac{1}{|z|} right) = infty$$






share|cite|improve this answer





























    4














    We have that by $t=x-2y to 0$ we reduce to the simpler



    $$large e^{frac{|x-2y|}{(x-2y)^2}}=e^{{|t|}/{t^2}}=e^{{1}/{|t|}}to e^infty=infty$$






    share|cite|improve this answer





















      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3040269%2fdetermining-lim-x-y-to-2y-y-exp-fracx-2yx-2y2%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      5














      It is :



      $$lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{(x-2y)^2}}right) = lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{|x-2y|^2}}right)$$
      $$=$$
      $$lim_{(x,y) to (2y,y)} expleft({frac{1}{|x-2y|}}right) equiv lim_{z to 0} expleft(frac{1}{|z|} right) = infty$$






      share|cite|improve this answer


























        5














        It is :



        $$lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{(x-2y)^2}}right) = lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{|x-2y|^2}}right)$$
        $$=$$
        $$lim_{(x,y) to (2y,y)} expleft({frac{1}{|x-2y|}}right) equiv lim_{z to 0} expleft(frac{1}{|z|} right) = infty$$






        share|cite|improve this answer
























          5












          5








          5






          It is :



          $$lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{(x-2y)^2}}right) = lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{|x-2y|^2}}right)$$
          $$=$$
          $$lim_{(x,y) to (2y,y)} expleft({frac{1}{|x-2y|}}right) equiv lim_{z to 0} expleft(frac{1}{|z|} right) = infty$$






          share|cite|improve this answer












          It is :



          $$lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{(x-2y)^2}}right) = lim_{(x,y) to (2y,y)} expleft({frac{|x-2y|}{|x-2y|^2}}right)$$
          $$=$$
          $$lim_{(x,y) to (2y,y)} expleft({frac{1}{|x-2y|}}right) equiv lim_{z to 0} expleft(frac{1}{|z|} right) = infty$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 15 at 8:53









          Rebellos

          14.2k31244




          14.2k31244























              4














              We have that by $t=x-2y to 0$ we reduce to the simpler



              $$large e^{frac{|x-2y|}{(x-2y)^2}}=e^{{|t|}/{t^2}}=e^{{1}/{|t|}}to e^infty=infty$$






              share|cite|improve this answer


























                4














                We have that by $t=x-2y to 0$ we reduce to the simpler



                $$large e^{frac{|x-2y|}{(x-2y)^2}}=e^{{|t|}/{t^2}}=e^{{1}/{|t|}}to e^infty=infty$$






                share|cite|improve this answer
























                  4












                  4








                  4






                  We have that by $t=x-2y to 0$ we reduce to the simpler



                  $$large e^{frac{|x-2y|}{(x-2y)^2}}=e^{{|t|}/{t^2}}=e^{{1}/{|t|}}to e^infty=infty$$






                  share|cite|improve this answer












                  We have that by $t=x-2y to 0$ we reduce to the simpler



                  $$large e^{frac{|x-2y|}{(x-2y)^2}}=e^{{|t|}/{t^2}}=e^{{1}/{|t|}}to e^infty=infty$$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 15 at 10:05









                  gimusi

                  1




                  1






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.





                      Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                      Please pay close attention to the following guidance:


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3040269%2fdetermining-lim-x-y-to-2y-y-exp-fracx-2yx-2y2%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      Popular posts from this blog

                      Сан-Квентин

                      Алькесар

                      Josef Freinademetz