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How do I show a limit at some point exists using the delta-epsilon definition, if I do not know what it's value is?
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How do I show a limit at some point exists using the delta-epsilon definition, if I do not know what it's value is?
For example how should I work with $limlimits_ (x,y) to (0,0) (e^x^y - 1)/y $? Even if you are able to identify its value, how would you go about it if you couldn't?
limits multivariable-calculus
edited Aug 5 at 23:36
Shaun
7,41792972
asked Aug 5 at 23:08
Fotis Rokanis
385
 |Â
show 3 more comments
up vote
0
down vote
favorite
How do I show a limit at some point exists using the delta-epsilon definition, if I do not know what it's value is?
For example how should I work with $limlimits_ (x,y) to (0,0) (e^x^y - 1)/y $? Even if you are able to identify its value, how would you go about it if you couldn't?
limits multivariable-calculus
edited Aug 5 at 23:36
Shaun
7,41792972
asked Aug 5 at 23:08
Fotis Rokanis
385
Here's a MathJax tutorial :)
– Shaun
Aug 5 at 23:10
Thanks a lot :D
– Fotis Rokanis
Aug 5 at 23:10
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
– Shaun
Aug 5 at 23:11
2
I think, in such a case, you would need to have a value of the limit in mind. $epsilon-delta$ proofs often hinge on 'working backwards from your conclusion', i.e., backing out the value of $delta$ needed to make the algebra work out. So, usually you would probably compute the limit by conventional means, and then prove it formally. At least, this is what is done in my experience.
– Matt.P
Aug 5 at 23:12
2
Please edit the question to make the limit more clear.
– Shaun
Aug 5 at 23:12
 |Â
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How do I show a limit at some point exists using the delta-epsilon definition, if I do not know what it's value is?
For example how should I work with $limlimits_ (x,y) to (0,0) (e^x^y - 1)/y $? Even if you are able to identify its value, how would you go about it if you couldn't?
limits multivariable-calculus
edited Aug 5 at 23:36
Shaun
7,41792972
asked Aug 5 at 23:08
Fotis Rokanis
385
How do I show a limit at some point exists using the delta-epsilon definition, if I do not know what it's value is?
For example how should I work with $limlimits_ (x,y) to (0,0) (e^x^y - 1)/y $? Even if you are able to identify its value, how would you go about it if you couldn't?
limits multivariable-calculus
edited Aug 5 at 23:36
Shaun
7,41792972
asked Aug 5 at 23:08
Fotis Rokanis
385
edited Aug 5 at 23:36
Shaun
7,41792972
edited Aug 5 at 23:36
Shaun
7,41792972
edited Aug 5 at 23:36
Shaun
7,41792972
7,41792972
asked Aug 5 at 23:08
Fotis Rokanis
385
asked Aug 5 at 23:08
Fotis Rokanis
385
asked Aug 5 at 23:08
Fotis Rokanis
385
385
Here's a MathJax tutorial :)
– Shaun
Aug 5 at 23:10
Thanks a lot :D
– Fotis Rokanis
Aug 5 at 23:10
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
– Shaun
Aug 5 at 23:11
2
I think, in such a case, you would need to have a value of the limit in mind. $epsilon-delta$ proofs often hinge on 'working backwards from your conclusion', i.e., backing out the value of $delta$ needed to make the algebra work out. So, usually you would probably compute the limit by conventional means, and then prove it formally. At least, this is what is done in my experience.
– Matt.P
Aug 5 at 23:12
2
Please edit the question to make the limit more clear.
– Shaun
Aug 5 at 23:12
 |Â
show 3 more comments
Here's a MathJax tutorial :)
– Shaun
Aug 5 at 23:10
Thanks a lot :D
– Fotis Rokanis
Aug 5 at 23:10
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
– Shaun
Aug 5 at 23:11
2
I think, in such a case, you would need to have a value of the limit in mind. $epsilon-delta$ proofs often hinge on 'working backwards from your conclusion', i.e., backing out the value of $delta$ needed to make the algebra work out. So, usually you would probably compute the limit by conventional means, and then prove it formally. At least, this is what is done in my experience.
– Matt.P
Aug 5 at 23:12
2
Please edit the question to make the limit more clear.
– Shaun
Aug 5 at 23:12
Here's a MathJax tutorial :)
– Shaun
Aug 5 at 23:10
Here's a MathJax tutorial :)
– Shaun
Aug 5 at 23:10
Thanks a lot :D
– Fotis Rokanis
Aug 5 at 23:10
Thanks a lot :D
– Fotis Rokanis
Aug 5 at 23:10
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
– Shaun
Aug 5 at 23:11
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
– Shaun
Aug 5 at 23:11
2
2
I think, in such a case, you would need to have a value of the limit in mind. $epsilon-delta$ proofs often hinge on 'working backwards from your conclusion', i.e., backing out the value of $delta$ needed to make the algebra work out. So, usually you would probably compute the limit by conventional means, and then prove it formally. At least, this is what is done in my experience.
– Matt.P
Aug 5 at 23:12
I think, in such a case, you would need to have a value of the limit in mind. $epsilon-delta$ proofs often hinge on 'working backwards from your conclusion', i.e., backing out the value of $delta$ needed to make the algebra work out. So, usually you would probably compute the limit by conventional means, and then prove it formally. At least, this is what is done in my experience.
– Matt.P
Aug 5 at 23:12
2
2
Please edit the question to make the limit more clear.
– Shaun
Aug 5 at 23:12
Please edit the question to make the limit more clear.
– Shaun
Aug 5 at 23:12
 |Â
show 3 more comments
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Here's a MathJax tutorial :)
– Shaun
Aug 5 at 23:10
Thanks a lot :D
– Fotis Rokanis
Aug 5 at 23:10
Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here.
– Shaun
Aug 5 at 23:11
2
I think, in such a case, you would need to have a value of the limit in mind. $epsilon-delta$ proofs often hinge on 'working backwards from your conclusion', i.e., backing out the value of $delta$ needed to make the algebra work out. So, usually you would probably compute the limit by conventional means, and then prove it formally. At least, this is what is done in my experience.
– Matt.P
Aug 5 at 23:12
2
Please edit the question to make the limit more clear.
– Shaun
Aug 5 at 23:12