I am not being able to solve this problem of Continuity. [closed]

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Prove that $[x] sin^2(pi x)$ is continuous at every integer point and
$[x] cos^2 (pi x)$ is discontinuous at every integer point.




real-analysis continuity discontinuous-functions




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closed as off-topic by Andrés E. Caicedo, José Carlos Santos, Tanner Swett, amWhy, Xander Henderson Aug 28 at 0:27


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Tanner Swett, amWhy, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.












  • What does $[x]$ mean?
    – Arthur
    Aug 27 at 14:07










  • Please use MathJax, I actually don't know what this [x] in brackets is supposed to denote.
    – Luke
    Aug 27 at 14:07










  • I'm guessing it should be the nearest integer to $x$.
    – Sobi
    Aug 27 at 14:11










  • It is common notation for the floor function, the greatest integer $leq x$.
    – Clayton
    Aug 27 at 14:20














up vote
-2
down vote

favorite












Prove that $[x] sin^2(pi x)$ is continuous at every integer point and
$[x] cos^2 (pi x)$ is discontinuous at every integer point.




real-analysis continuity discontinuous-functions




share|cite|improve this question














closed as off-topic by Andrés E. Caicedo, José Carlos Santos, Tanner Swett, amWhy, Xander Henderson Aug 28 at 0:27


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Tanner Swett, amWhy, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.












  • What does $[x]$ mean?
    – Arthur
    Aug 27 at 14:07










  • Please use MathJax, I actually don't know what this [x] in brackets is supposed to denote.
    – Luke
    Aug 27 at 14:07










  • I'm guessing it should be the nearest integer to $x$.
    – Sobi
    Aug 27 at 14:11










  • It is common notation for the floor function, the greatest integer $leq x$.
    – Clayton
    Aug 27 at 14:20












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











Prove that $[x] sin^2(pi x)$ is continuous at every integer point and
$[x] cos^2 (pi x)$ is discontinuous at every integer point.




real-analysis continuity discontinuous-functions




share|cite|improve this question














Prove that $[x] sin^2(pi x)$ is continuous at every integer point and
$[x] cos^2 (pi x)$ is discontinuous at every integer point.





real-analysis continuity discontinuous-functions





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 27 at 14:20









Clayton

18.3k22883




18.3k22883










asked Aug 27 at 14:05









Sragdharamalini Das

227




227




closed as off-topic by Andrés E. Caicedo, José Carlos Santos, Tanner Swett, amWhy, Xander Henderson Aug 28 at 0:27


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Tanner Swett, amWhy, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Andrés E. Caicedo, José Carlos Santos, Tanner Swett, amWhy, Xander Henderson Aug 28 at 0:27


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, Tanner Swett, amWhy, Xander Henderson
If this question can be reworded to fit the rules in the help center, please edit the question.











  • What does $[x]$ mean?
    – Arthur
    Aug 27 at 14:07










  • Please use MathJax, I actually don't know what this [x] in brackets is supposed to denote.
    – Luke
    Aug 27 at 14:07










  • I'm guessing it should be the nearest integer to $x$.
    – Sobi
    Aug 27 at 14:11










  • It is common notation for the floor function, the greatest integer $leq x$.
    – Clayton
    Aug 27 at 14:20
















  • What does $[x]$ mean?
    – Arthur
    Aug 27 at 14:07










  • Please use MathJax, I actually don't know what this [x] in brackets is supposed to denote.
    – Luke
    Aug 27 at 14:07










  • I'm guessing it should be the nearest integer to $x$.
    – Sobi
    Aug 27 at 14:11










  • It is common notation for the floor function, the greatest integer $leq x$.
    – Clayton
    Aug 27 at 14:20















What does $[x]$ mean?
– Arthur
Aug 27 at 14:07




What does $[x]$ mean?
– Arthur
Aug 27 at 14:07












Please use MathJax, I actually don't know what this [x] in brackets is supposed to denote.
– Luke
Aug 27 at 14:07




Please use MathJax, I actually don't know what this [x] in brackets is supposed to denote.
– Luke
Aug 27 at 14:07












I'm guessing it should be the nearest integer to $x$.
– Sobi
Aug 27 at 14:11




I'm guessing it should be the nearest integer to $x$.
– Sobi
Aug 27 at 14:11












It is common notation for the floor function, the greatest integer $leq x$.
– Clayton
Aug 27 at 14:20




It is common notation for the floor function, the greatest integer $leq x$.
– Clayton
Aug 27 at 14:20










1 Answer
1






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oldest

votes

















up vote
1
down vote



accepted










Hint: $sin(pi x) = 0$ whenever $xinmathbbZ$ and $|cos(pi x)| = 1 not= 0$ whenever $x in mathbbZ.$






share|cite|improve this answer



























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    Hint: $sin(pi x) = 0$ whenever $xinmathbbZ$ and $|cos(pi x)| = 1 not= 0$ whenever $x in mathbbZ.$






    share|cite|improve this answer
























      up vote
      1
      down vote



      accepted










      Hint: $sin(pi x) = 0$ whenever $xinmathbbZ$ and $|cos(pi x)| = 1 not= 0$ whenever $x in mathbbZ.$






      share|cite|improve this answer






















        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        Hint: $sin(pi x) = 0$ whenever $xinmathbbZ$ and $|cos(pi x)| = 1 not= 0$ whenever $x in mathbbZ.$






        share|cite|improve this answer












        Hint: $sin(pi x) = 0$ whenever $xinmathbbZ$ and $|cos(pi x)| = 1 not= 0$ whenever $x in mathbbZ.$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 27 at 14:10









        Sobi

        2,428315




        2,428315












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