In Calculus, what are the terms for the different parts of Limit notation: specifically, is there a term for "the value that we are approaching". For reference, fractions have a numerator and a denominator; radicals have an index, radical sign and radicand. Thanks in advance!
Terms for parts of Limit expressions (specifically, what x is tending toward)
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mmm4444bot
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If a limit exists, then it's the fixed value that a function output's approach. So, if you're asking what to call that number, it's called "the limit".
If you're asking instead whether there's a name for the value approached by the function's inputs, then I can't remember seeing a specific name for that.
EG:
\(\displaystyle \displaystyle \lim_{x\to4} x^2 = 16\)
16 is the limit
I don't know whether 4 has a name
If you're asking instead whether there's a name for the value approached by the function's inputs, then I can't remember seeing a specific name for that.
EG:
\(\displaystyle \displaystyle \lim_{x\to4} x^2 = 16\)
16 is the limit
I don't know whether 4 has a name
Thanks for the quick reply!
Unfortunately, in your example, the 4 that x is approaching is exactly the item that I'm looking for terminology for. It wasn't given in my class, and none of the reference materials I've found so far online give a name to it. I just find it so odd because most other subjects in mathematics that I've learned have gone to great lengths to give names to parts of everything so that it is easier to write about when referencing it. If anybody else has an idea, i'm still searching. Thanks.
Unfortunately, in your example, the 4 that x is approaching is exactly the item that I'm looking for terminology for. It wasn't given in my class, and none of the reference materials I've found so far online give a name to it. I just find it so odd because most other subjects in mathematics that I've learned have gone to great lengths to give names to parts of everything so that it is easier to write about when referencing it. If anybody else has an idea, i'm still searching. Thanks.
Dr.Peterson
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Generally, when something doesn't have a well-known name, it is because no particular need has been found for one, either because we seldom talk about it directly, or because short phrases work well enough.
Can you give an example of a sentence in which you would want to use such a term? Maybe pretend that the word is "limitend", and try using that.
I can't think of any theorems or other statements we would need the term for, unless it was something like "When the limitend is infinite, ...", for which we would just say, "If it is a limit at infinity, ...," or "if x is approaching infinity, ...," or something like that. Or, if the context mentioned lim_{x->a}, we would just refer to the "limitend" as "a". Or, I suppose, you might want to say, "If the function is continuous, you can just replace the variable with the limitend." Is that the sort of situation you have in mind?
On the other side of the question, if I were to make up a term, I would derive it from a Latin word meaning "that which is to be approached", and a quick search suggests only "propinquend", which doesn't appeal to me very much. Or maybe just an English word, like "the location of the limit", or terminus, or target. But nothing I think of seems like what we might actually use.
I like limitend or target. A use of the word in a sentence would be when teaching or reflecting on a limit for teaching or research purposes and probably more useful when writing rather than speaking.
Ex: "It matters what your limitend is; if the limitend is +/- infinity, then you can ignore non-significant terms. If your limitend has superscript + (the plus sign meaning from the right), then a limit can be found at Vertical Asymptotes where standard limits Do Not Exist. If the limitend is a negative infinity, then be mindful of your signs. Always check your discontinuities, because the limitend may not be a problem and you don't want to have to do more work than is necessary. Once you 'plug in' the limitend, you no longer write the limit notation because you are now evaluating the limit, not working with it."