How can I find $delta$ given $epsilon$?

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How do I need to show that there exist $delta>0$ corresponding to $epsilon= 0.03$, when $(x,y,z)to (0,0,0)$ using $epsilon$-$delta$ definition of limit. Given that $f(x,y,z)$ is
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$










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  • Why this $z$ ??
    – Yves Daoust
    Aug 31 at 8:00











  • I tried to say that but was not sure how to stretch the comment to 15 characters.
    – badjohn
    Aug 31 at 8:02










  • Thanks, now I know.
    – badjohn
    Aug 31 at 8:04










  • @Sumit Please check if my edit is correct.
    – Robert Z
    Aug 31 at 8:13










  • Its absolutely correct. Thank you :)
    – Sumit
    Aug 31 at 9:12














up vote
-1
down vote

favorite












How do I need to show that there exist $delta>0$ corresponding to $epsilon= 0.03$, when $(x,y,z)to (0,0,0)$ using $epsilon$-$delta$ definition of limit. Given that $f(x,y,z)$ is
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$










share|cite|improve this question























  • Why this $z$ ??
    – Yves Daoust
    Aug 31 at 8:00











  • I tried to say that but was not sure how to stretch the comment to 15 characters.
    – badjohn
    Aug 31 at 8:02










  • Thanks, now I know.
    – badjohn
    Aug 31 at 8:04










  • @Sumit Please check if my edit is correct.
    – Robert Z
    Aug 31 at 8:13










  • Its absolutely correct. Thank you :)
    – Sumit
    Aug 31 at 9:12












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











How do I need to show that there exist $delta>0$ corresponding to $epsilon= 0.03$, when $(x,y,z)to (0,0,0)$ using $epsilon$-$delta$ definition of limit. Given that $f(x,y,z)$ is
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$










share|cite|improve this question















How do I need to show that there exist $delta>0$ corresponding to $epsilon= 0.03$, when $(x,y,z)to (0,0,0)$ using $epsilon$-$delta$ definition of limit. Given that $f(x,y,z)$ is
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$







calculus limits continuity math-software piecewise-continuity






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edited Aug 31 at 8:12









Robert Z

85.6k1055123




85.6k1055123










asked Aug 31 at 7:57









Sumit

62




62











  • Why this $z$ ??
    – Yves Daoust
    Aug 31 at 8:00











  • I tried to say that but was not sure how to stretch the comment to 15 characters.
    – badjohn
    Aug 31 at 8:02










  • Thanks, now I know.
    – badjohn
    Aug 31 at 8:04










  • @Sumit Please check if my edit is correct.
    – Robert Z
    Aug 31 at 8:13










  • Its absolutely correct. Thank you :)
    – Sumit
    Aug 31 at 9:12
















  • Why this $z$ ??
    – Yves Daoust
    Aug 31 at 8:00











  • I tried to say that but was not sure how to stretch the comment to 15 characters.
    – badjohn
    Aug 31 at 8:02










  • Thanks, now I know.
    – badjohn
    Aug 31 at 8:04










  • @Sumit Please check if my edit is correct.
    – Robert Z
    Aug 31 at 8:13










  • Its absolutely correct. Thank you :)
    – Sumit
    Aug 31 at 9:12















Why this $z$ ??
– Yves Daoust
Aug 31 at 8:00





Why this $z$ ??
– Yves Daoust
Aug 31 at 8:00













I tried to say that but was not sure how to stretch the comment to 15 characters.
– badjohn
Aug 31 at 8:02




I tried to say that but was not sure how to stretch the comment to 15 characters.
– badjohn
Aug 31 at 8:02












Thanks, now I know.
– badjohn
Aug 31 at 8:04




Thanks, now I know.
– badjohn
Aug 31 at 8:04












@Sumit Please check if my edit is correct.
– Robert Z
Aug 31 at 8:13




@Sumit Please check if my edit is correct.
– Robert Z
Aug 31 at 8:13












Its absolutely correct. Thank you :)
– Sumit
Aug 31 at 9:12




Its absolutely correct. Thank you :)
– Sumit
Aug 31 at 9:12










1 Answer
1






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up vote
0
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Hint:



This plot of $dfractan xx$ shows you that you can ensure $c_0|t|le|tan t|le c_1|t|$ in your favorite range around $0$ ($c_0=1,c_1=tan x_max/x_max$). With this you can easily bound.



enter image description here






share|cite|improve this answer






















  • Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
    – Sumit
    Aug 31 at 8:22










  • @Sumit: could you solve for the function $x^2+y^2+z^2$ ?
    – Yves Daoust
    Aug 31 at 8:27











  • yes I can for $x^2+y^2+z^2$
    – Sumit
    Aug 31 at 8:33











  • @Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
    – Yves Daoust
    Aug 31 at 8:35










  • yup, I can. Thanks
    – Sumit
    Aug 31 at 8:39










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













Hint:



This plot of $dfractan xx$ shows you that you can ensure $c_0|t|le|tan t|le c_1|t|$ in your favorite range around $0$ ($c_0=1,c_1=tan x_max/x_max$). With this you can easily bound.



enter image description here






share|cite|improve this answer






















  • Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
    – Sumit
    Aug 31 at 8:22










  • @Sumit: could you solve for the function $x^2+y^2+z^2$ ?
    – Yves Daoust
    Aug 31 at 8:27











  • yes I can for $x^2+y^2+z^2$
    – Sumit
    Aug 31 at 8:33











  • @Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
    – Yves Daoust
    Aug 31 at 8:35










  • yup, I can. Thanks
    – Sumit
    Aug 31 at 8:39














up vote
0
down vote













Hint:



This plot of $dfractan xx$ shows you that you can ensure $c_0|t|le|tan t|le c_1|t|$ in your favorite range around $0$ ($c_0=1,c_1=tan x_max/x_max$). With this you can easily bound.



enter image description here






share|cite|improve this answer






















  • Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
    – Sumit
    Aug 31 at 8:22










  • @Sumit: could you solve for the function $x^2+y^2+z^2$ ?
    – Yves Daoust
    Aug 31 at 8:27











  • yes I can for $x^2+y^2+z^2$
    – Sumit
    Aug 31 at 8:33











  • @Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
    – Yves Daoust
    Aug 31 at 8:35










  • yup, I can. Thanks
    – Sumit
    Aug 31 at 8:39












up vote
0
down vote










up vote
0
down vote









Hint:



This plot of $dfractan xx$ shows you that you can ensure $c_0|t|le|tan t|le c_1|t|$ in your favorite range around $0$ ($c_0=1,c_1=tan x_max/x_max$). With this you can easily bound.



enter image description here






share|cite|improve this answer














Hint:



This plot of $dfractan xx$ shows you that you can ensure $c_0|t|le|tan t|le c_1|t|$ in your favorite range around $0$ ($c_0=1,c_1=tan x_max/x_max$). With this you can easily bound.



enter image description here







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Aug 31 at 8:13

























answered Aug 31 at 8:06









Yves Daoust

114k665209




114k665209











  • Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
    – Sumit
    Aug 31 at 8:22










  • @Sumit: could you solve for the function $x^2+y^2+z^2$ ?
    – Yves Daoust
    Aug 31 at 8:27











  • yes I can for $x^2+y^2+z^2$
    – Sumit
    Aug 31 at 8:33











  • @Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
    – Yves Daoust
    Aug 31 at 8:35










  • yup, I can. Thanks
    – Sumit
    Aug 31 at 8:39
















  • Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
    – Sumit
    Aug 31 at 8:22










  • @Sumit: could you solve for the function $x^2+y^2+z^2$ ?
    – Yves Daoust
    Aug 31 at 8:27











  • yes I can for $x^2+y^2+z^2$
    – Sumit
    Aug 31 at 8:33











  • @Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
    – Yves Daoust
    Aug 31 at 8:35










  • yup, I can. Thanks
    – Sumit
    Aug 31 at 8:39















Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
– Sumit
Aug 31 at 8:22




Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
– Sumit
Aug 31 at 8:22












@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
– Yves Daoust
Aug 31 at 8:27





@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
– Yves Daoust
Aug 31 at 8:27













yes I can for $x^2+y^2+z^2$
– Sumit
Aug 31 at 8:33





yes I can for $x^2+y^2+z^2$
– Sumit
Aug 31 at 8:33













@Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
– Yves Daoust
Aug 31 at 8:35




@Sumit: so you could for $c_1^2x^2+c_1^2y^2+c_1^2z^2$, couldn't you ?
– Yves Daoust
Aug 31 at 8:35












yup, I can. Thanks
– Sumit
Aug 31 at 8:39




yup, I can. Thanks
– Sumit
Aug 31 at 8:39

















 

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