Limits: What is "a" in the Equation?

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In summary, the name for "a" in the given example of a limit as x approaches a is often referred to as "a point". However, this term is not particularly special and is not necessarily limited to values in the domain of a function. Other terms such as "value that x approaches" or simply "a" may also be used. It all depends on context and personal preference.
  • #1
Madeline
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I was wondering what the name for "a" is in the following example.

The limit as x approaches a of (any function).
 
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  • #2
I don't think it has a specific name. Could be wrong, though.
 
  • #3
I don't know of any name for it either.
 
  • #4
It's called "the value that x approaches"... duh :tongue2:
 
  • #5
Madeline said:
I was wondering what the name for "a" is in the following example.

The limit as x approaches a of (any function).

"a" would be called "a point" as in "the limit of f at a point". Of course that's not a particularly special name.
 
  • #6
Thanks for all your replies. I was trying to word my response to a homework question last night. It doesn't really matter at all though, but I was curious.
 
  • #7
jcsd said:
"a" would be called "a point" as in "the limit of f at a point". Of course that's not a particularly special name.

Saying "point" almost implies that the limit is equal to the value of f at that point. At least that's what I think of. "A" isn't exactly a point, it's just a value in the domain.
 
  • #8
Madeline said:
Saying "point" almost implies that the limit is equal to the value of f at that point. At least that's what I think of. "A" isn't exactly a point, it's just a value in the domain.

There's reason for calling it a point, a limit requires that the domain (and the range) has more structure than a primitve concept of a set; the members of the mathematical structures we require are often called points. It may almost imply something to you, but it doesn't generally as it's standard usuage.


ps a minor quibble: "a" needn't lie in the domain of some function "f" for the limit of "f" at "a" to exist.
 
  • #9
I think it is usually named "Howard", but occasionally "Ozymandias".
 
  • #10
jcsd said:
There's reason for calling it a point, a limit requires that the domain (and the range) has more structure than a primitve concept of a set; the members of the mathematical structures we require are often called points. It may almost imply something to you, but it doesn't generally as it's standard usuage.

I see, I didn't realize this was a standard term.

ps a minor quibble: "a" needn't lie in the domain of some function "f" for the limit of "f" at "a" to exist.

Oh yeah, I forgot about that :). I guess what I mean to say is that point implies that there is a "point" at "a" which would mean that a is in the domain of f. But you were right that if point is standard usage, then it doesn't really matter what it implies.
 

1. What is the value of "a" in the equation?

The value of "a" in an equation represents the coefficient or the number that is multiplied by the variable. It can also be thought of as the rate of change or slope.

2. How does "a" affect the graph of an equation?

The value of "a" determines the steepness or slope of the graph of an equation. If "a" is a positive number, the graph will have an upward slope, and if "a" is a negative number, the graph will have a downward slope.

3. Can "a" ever be equal to 0?

Yes, "a" can be equal to 0. In this case, the variable is eliminated from the equation, and the resulting graph will be a straight line with no slope.

4. How do you solve for "a" in an equation?

To solve for "a" in an equation, you would need to isolate it on one side of the equation by performing inverse operations. For example, if "a" is being added to both sides of the equation, you would subtract "a" from both sides to isolate it.

5. What is the significance of "a" in the context of limits?

In the context of limits, "a" represents the value that a function is approaching as the input (x) approaches a certain value. This value can be used to determine the behavior of the function and if it has a limit at that point.

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