Does it make sense to talk about limit in this case?
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
edited 2 days ago
zipirovich
11.1k11631
asked 2 days ago
Юрій ЯрошЮрій Ярош
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add a comment |
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
edited 2 days ago
zipirovich
11.1k11631
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
add a comment |
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
edited 2 days ago
zipirovich
11.1k11631
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
Suppose I have a function that is defined only for values bigger than $a$, does it make sense to talk about limit of a function at that point, or only about limit from the right? It seems to me that we can talk about limit of a function, because if we look at the definition
$$forall epsilon>0 ; exists delta>0 ; forall xin A: ; 0<|x-a|<delta Rightarrow |f(x)-L|<epsilon$$
($A$ is domain of the function), we have the requirement of $x$ being in the domain and so limit still would make sense. But I am not sure.
Thanks in advance.
real-analysis limits
real-analysis limits
edited 2 days ago
zipirovich
11.1k11631
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
edited 2 days ago
zipirovich
11.1k11631
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
edited 2 days ago
zipirovich
11.1k11631
edited 2 days ago
zipirovich
11.1k11631
edited 2 days ago
zipirovich
11.1k11631
11.1k11631
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
asked 2 days ago
Юрій ЯрошЮрій Ярош
1,071615
1,071615
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered 2 days ago
John OmielanJohn Omielan
1,19918
add a comment |
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered 2 days ago
John OmielanJohn Omielan
1,19918
add a comment |
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered 2 days ago
John OmielanJohn Omielan
1,19918
add a comment |
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered 2 days ago
John OmielanJohn Omielan
1,19918
If a function is not defined for values smaller than or equal to $a$, then you can't deal with anything in that range of values. As such, for limits, you can certainly talk about a limit from the right. A general "limit" would either be considered to not exist, but I believe it would usually mean determining it only from the right, as mentioned. This might depend, to some extent, on the specific context in which the limit is being asked about. I hope this answers what you're specifically asking about.
answered 2 days ago
John OmielanJohn Omielan
1,19918
answered 2 days ago
John OmielanJohn Omielan
1,19918
answered 2 days ago
John OmielanJohn Omielan
1,19918
answered 2 days ago
John OmielanJohn Omielan
1,19918
1,19918
add a comment |
add a comment |
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
add a comment |
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
add a comment |
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
Yes, you are right. In such a case, the concepts of limit and right-hand limit coincide.
For example, it doesn't make any difference whether you write
$$
lim_{x to 0} sqrt{x} = 0
$$
or
$$
lim_{x to 0^+} sqrt{x} = 0
.
$$
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
answered 2 days ago
Hans LundmarkHans Lundmark
35.2k564114
35.2k564114
add a comment |
add a comment |
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