1

Consider $\int x^2 dx$. The function being integrated has a name, namely the integrand.

Is there a corresponding term for the function whose limit is being taken?

For example, if I have $$\lim_{x \to 1} \frac {x^2 - 1}{x -1}$$ is there a term to say "The function whose limit is being taken, namely $\frac {x^2 - 1}{x -1}$, is equal to $x + 1$ when $x \neq 1$."

SRobertJames
  • 4,278
  • 1
  • 11
  • 27
  • 2
    Related: https://math.stackexchange.com/questions/1028296/whats-a-concise-word-for-the-expression-inside-a-limit-limitand – Andreas Lenz Jul 14 '23 at 16:29
  • 2
    I try to get students away from thinking about limits as an operation on functions (like the integral), and towards a relation between functions and values. In the first framework you have to deal with this nebulous "DNE" limit, while in the second you can just say it's not related to any particular value. Your question is still a good one though! – Matthew Leingang Jul 14 '23 at 16:31
  • Argument? Not standard, but at least one place where it's used. – Sarvesh Ravichandran Iyer Jul 14 '23 at 16:45
  • The word "integrand" is useful because there are two functions under discussion: the integrand and the antiderivative (or bunch thereof, etc.). For a limit, there is typically only one function under discussion; so 90+% of the time (including in your example), you could simply say "the function". – Mark S. Jul 15 '23 at 00:56

0 Answers0