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
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$
calculus limits continuity math-software piecewise-continuity
add a comment |Â
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
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$
calculus limits continuity math-software piecewise-continuity
Why this $z$ ??
â Yves Daoust
Aug 31 at 8:00
I tried to say that but was not sure how to stretch the comment to 15 characters.
â badjohn
Aug 31 at 8:02
Thanks, now I know.
â badjohn
Aug 31 at 8:04
@Sumit Please check if my edit is correct.
â Robert Z
Aug 31 at 8:13
Its absolutely correct. Thank you :)
â Sumit
Aug 31 at 9:12
add a comment |Â
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
$$f(x,y,z)=tan^2 x + tan^2 y + tan^2 z.$$
calculus limits continuity math-software piecewise-continuity
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
calculus limits continuity math-software piecewise-continuity
edited Aug 31 at 8:12
Robert Z
85.6k1055123
85.6k1055123
asked Aug 31 at 7:57
Sumit
62
62
Why this $z$ ??
â Yves Daoust
Aug 31 at 8:00
I tried to say that but was not sure how to stretch the comment to 15 characters.
â badjohn
Aug 31 at 8:02
Thanks, now I know.
â badjohn
Aug 31 at 8:04
@Sumit Please check if my edit is correct.
â Robert Z
Aug 31 at 8:13
Its absolutely correct. Thank you :)
â Sumit
Aug 31 at 9:12
add a comment |Â
Why this $z$ ??
â Yves Daoust
Aug 31 at 8:00
I tried to say that but was not sure how to stretch the comment to 15 characters.
â badjohn
Aug 31 at 8:02
Thanks, now I know.
â badjohn
Aug 31 at 8:04
@Sumit Please check if my edit is correct.
â Robert Z
Aug 31 at 8:13
Its absolutely correct. Thank you :)
â Sumit
Aug 31 at 9:12
Why this $z$ ??
â Yves Daoust
Aug 31 at 8:00
Why this $z$ ??
â Yves Daoust
Aug 31 at 8:00
I tried to say that but was not sure how to stretch the comment to 15 characters.
â badjohn
Aug 31 at 8:02
I tried to say that but was not sure how to stretch the comment to 15 characters.
â badjohn
Aug 31 at 8:02
Thanks, now I know.
â badjohn
Aug 31 at 8:04
Thanks, now I know.
â badjohn
Aug 31 at 8:04
@Sumit Please check if my edit is correct.
â Robert Z
Aug 31 at 8:13
@Sumit Please check if my edit is correct.
â Robert Z
Aug 31 at 8:13
Its absolutely correct. Thank you :)
â Sumit
Aug 31 at 9:12
Its absolutely correct. Thank you :)
â Sumit
Aug 31 at 9:12
add a comment |Â
1 Answer
1
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.
Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
â Sumit
Aug 31 at 8:22
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
yes I can for $x^2+y^2+z^2$
â 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 ?
â Yves Daoust
Aug 31 at 8:35
yup, I can. Thanks
â Sumit
Aug 31 at 8:39
add a comment |Â
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.
Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
â Sumit
Aug 31 at 8:22
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
yes I can for $x^2+y^2+z^2$
â 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 ?
â Yves Daoust
Aug 31 at 8:35
yup, I can. Thanks
â Sumit
Aug 31 at 8:39
add a comment |Â
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.
Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
â Sumit
Aug 31 at 8:22
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
yes I can for $x^2+y^2+z^2$
â 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 ?
â Yves Daoust
Aug 31 at 8:35
yup, I can. Thanks
â Sumit
Aug 31 at 8:39
add a comment |Â
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.
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.
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.
â Sumit
Aug 31 at 8:22
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
yes I can for $x^2+y^2+z^2$
â 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 ?
â Yves Daoust
Aug 31 at 8:35
yup, I can. Thanks
â Sumit
Aug 31 at 8:39
add a comment |Â
Thank you, but would you please elaborate till finding a delta corresponding to epsilon=0.03. Please I need to understand it.
â Sumit
Aug 31 at 8:22
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
yes I can for $x^2+y^2+z^2$
â 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 ?
â Yves Daoust
Aug 31 at 8:35
yup, I can. Thanks
â 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.
â 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.
â Sumit
Aug 31 at 8:22
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
@Sumit: could you solve for the function $x^2+y^2+z^2$ ?
â Yves Daoust
Aug 31 at 8:27
yes I can for $x^2+y^2+z^2$
â Sumit
Aug 31 at 8:33
yes I can for $x^2+y^2+z^2$
â 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 ?
â 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 ?
â Yves Daoust
Aug 31 at 8:35
yup, I can. Thanks
â Sumit
Aug 31 at 8:39
yup, I can. Thanks
â Sumit
Aug 31 at 8:39
add a comment |Â
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Why this $z$ ??
â Yves Daoust
Aug 31 at 8:00
I tried to say that but was not sure how to stretch the comment to 15 characters.
â badjohn
Aug 31 at 8:02
Thanks, now I know.
â badjohn
Aug 31 at 8:04
@Sumit Please check if my edit is correct.
â Robert Z
Aug 31 at 8:13
Its absolutely correct. Thank you :)
â Sumit
Aug 31 at 9:12