In a function such that $f(x)=frac1x^2$ would the limit as $x$ approaches zero be infinity or would it not exist?
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If you have a function such as $f(x)=frac1x^2$ , would the limit be infinity or would it not exist. A textbook I had said it was infinity but I feel like it does not exist because infinity is not a specific numeric value. So what is the limit for such an equation?
calculus limits rational-functions
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
asked Sep 11 at 2:09
Daniel Lee
91
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If you have a function such as $f(x)=frac1x^2$ , would the limit be infinity or would it not exist. A textbook I had said it was infinity but I feel like it does not exist because infinity is not a specific numeric value. So what is the limit for such an equation?
calculus limits rational-functions
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
asked Sep 11 at 2:09
Daniel Lee
91
Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Sep 11 at 2:18
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If you have a function such as $f(x)=frac1x^2$ , would the limit be infinity or would it not exist. A textbook I had said it was infinity but I feel like it does not exist because infinity is not a specific numeric value. So what is the limit for such an equation?
calculus limits rational-functions
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
asked Sep 11 at 2:09
Daniel Lee
91
If you have a function such as $f(x)=frac1x^2$ , would the limit be infinity or would it not exist. A textbook I had said it was infinity but I feel like it does not exist because infinity is not a specific numeric value. So what is the limit for such an equation?
calculus limits rational-functions
calculus limits rational-functions
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
asked Sep 11 at 2:09
Daniel Lee
91
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
asked Sep 11 at 2:09
Daniel Lee
91
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
edited Sep 11 at 2:17
Ahmad Bazzi
7,4912724
7,4912724
asked Sep 11 at 2:09
Daniel Lee
91
asked Sep 11 at 2:09
Daniel Lee
91
asked Sep 11 at 2:09
Daniel Lee
91
91
Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Sep 11 at 2:18
add a comment |
Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Sep 11 at 2:18
Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Sep 11 at 2:18
Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Sep 11 at 2:18
add a comment |
2 Answers
2
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It depends on the author's persuasion. Really, saying something like $lim_x to 0 frac1x^2 = +infty$ is just short-hand for "the limit does not exist but here's why." The function consistently blows up from either side of $0$, so that's how you report it. But, it definitely does not exist, even though you write it as "equal" to something.
This explains why the same author may write "$lim_x to 0 frac1x$ does not exist." Here, the function exhibits different/inconsistent behavior from each side: one blows up, one blows down. So, you can not report that it does something consistent around $0$ regardless of side, so you have no choice but to use the words.
To answer the question in your title, the answer is unfortunately "both." The limit does not exist because it approaches infinity.
answered Sep 11 at 2:20
Randall
8,44411028
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0
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Infinity is not really a number, at least not in standard analysis. The limit does not exist.
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
It depends on the author's persuasion. Really, saying something like $lim_x to 0 frac1x^2 = +infty$ is just short-hand for "the limit does not exist but here's why." The function consistently blows up from either side of $0$, so that's how you report it. But, it definitely does not exist, even though you write it as "equal" to something.
This explains why the same author may write "$lim_x to 0 frac1x$ does not exist." Here, the function exhibits different/inconsistent behavior from each side: one blows up, one blows down. So, you can not report that it does something consistent around $0$ regardless of side, so you have no choice but to use the words.
To answer the question in your title, the answer is unfortunately "both." The limit does not exist because it approaches infinity.
answered Sep 11 at 2:20
Randall
8,44411028
add a comment |
up vote
4
down vote
It depends on the author's persuasion. Really, saying something like $lim_x to 0 frac1x^2 = +infty$ is just short-hand for "the limit does not exist but here's why." The function consistently blows up from either side of $0$, so that's how you report it. But, it definitely does not exist, even though you write it as "equal" to something.
This explains why the same author may write "$lim_x to 0 frac1x$ does not exist." Here, the function exhibits different/inconsistent behavior from each side: one blows up, one blows down. So, you can not report that it does something consistent around $0$ regardless of side, so you have no choice but to use the words.
To answer the question in your title, the answer is unfortunately "both." The limit does not exist because it approaches infinity.
answered Sep 11 at 2:20
Randall
8,44411028
add a comment |
up vote
4
down vote
up vote
4
down vote
It depends on the author's persuasion. Really, saying something like $lim_x to 0 frac1x^2 = +infty$ is just short-hand for "the limit does not exist but here's why." The function consistently blows up from either side of $0$, so that's how you report it. But, it definitely does not exist, even though you write it as "equal" to something.
This explains why the same author may write "$lim_x to 0 frac1x$ does not exist." Here, the function exhibits different/inconsistent behavior from each side: one blows up, one blows down. So, you can not report that it does something consistent around $0$ regardless of side, so you have no choice but to use the words.
To answer the question in your title, the answer is unfortunately "both." The limit does not exist because it approaches infinity.
answered Sep 11 at 2:20
Randall
8,44411028
It depends on the author's persuasion. Really, saying something like $lim_x to 0 frac1x^2 = +infty$ is just short-hand for "the limit does not exist but here's why." The function consistently blows up from either side of $0$, so that's how you report it. But, it definitely does not exist, even though you write it as "equal" to something.
This explains why the same author may write "$lim_x to 0 frac1x$ does not exist." Here, the function exhibits different/inconsistent behavior from each side: one blows up, one blows down. So, you can not report that it does something consistent around $0$ regardless of side, so you have no choice but to use the words.
To answer the question in your title, the answer is unfortunately "both." The limit does not exist because it approaches infinity.
answered Sep 11 at 2:20
Randall
8,44411028
edited Sep 11 at 2:29
answered Sep 11 at 2:20
Randall
8,44411028
answered Sep 11 at 2:20
Randall
8,44411028
answered Sep 11 at 2:20
Randall
8,44411028
8,44411028
add a comment |
add a comment |
up vote
0
down vote
Infinity is not really a number, at least not in standard analysis. The limit does not exist.
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
add a comment |
up vote
0
down vote
Infinity is not really a number, at least not in standard analysis. The limit does not exist.
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
add a comment |
up vote
0
down vote
up vote
0
down vote
Infinity is not really a number, at least not in standard analysis. The limit does not exist.
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
Infinity is not really a number, at least not in standard analysis. The limit does not exist.
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
answered Sep 11 at 2:12
Oscar Lanzi
11.2k11935
11.2k11935
add a comment |
add a comment |
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Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Sep 11 at 2:18