# Questions tagged [limits]

For question regarding the properties and evaluation of limits.

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### "Real life" examples of limits of functions at finite points

This is more specific than this similar question on math.SE, since I'm not satisfied with the answers there. Question: Can you provide an interesting, natural and simple example of some physical/...
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### What would constitute as a good justification of why a divergent limit is divergence for highschool teaching?

For example, consider $\lim_{x \to -\infty} \frac{x}{e^x}$, what would constitute as a good justification that the limit diverges too infinity? It's pretty easy to justify convergent limits ...
631 views

### Process of finding limits for multivariable functions

I was tutoring a student today and they asked a question which made me curious. We were working on the following question together. After explaining that we must look at the limit along the x axis, I ...
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### Example of a phenomenon from real life where there is a limit going to infinity

I haven't been able to find examples in real life where we have a function or sequence such that the limit goes to infinity when the independent variable goes to infinity. The only one so far is ...
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### Is this motivation for the concept of a limit a good one?

tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my ...
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### Finite sum of infinite series

I have two issues related to finite sum of infinite series, 1) How you would to describe 2 when you talk about the infinite geometric series 1+ 1/2 + 1/4 + 1/8 + ..... 2) How you would compare using ...
1 vote
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### Introducing direct substitution in an intro calculus course

I'm revisiting the materials I've put together for students taking a non-proof-based intro to calculus, and my goal is for them to have a clear but rough sense of a limit as a bound (basically enough ...
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### Nice examples of limits to infinity in real life

I have to teach limits to infinity of real functions of one variable. I would like to start my course with a beautiful example, not simply a basic function like $1/x$. For instance, I thought of using ...
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1 vote
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### When teaching someone how to prove a function is uniformly continuous, using epsilon/delta, which example would be among the simplest?

I've taught how to use $\epsilon, \delta$ to prove that a function is continuous at a point, and I'm about to teach how to prove that a function is uniformly continuous over an open interval. Usually,...
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### About the word "limit" used in calculus

In the introduction of the limits chapter of a scholar book I can read (translated and abstract) the following examples: "the price of a product has a limit value that, from this price, the number of ...
280 views

### How to explain the concepts of limits and continuity to non-mathematical students

How can I explain the fundamental concepts of limits and continuity to a student with a non-mathematical background? I am a PhD student in Mathematics working in Differential Geometry. As a part of my ...
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### When should the limit be introduced?

Usually school children are taught fractions and decimal representations way before the notion of limit. So they must come to the idea that infinite decimal sequences like 0.999... are the same as an ...
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### Near-universal student mistake on $\lim_{x\rightarrow\infty}e^{x+1}/e^x$

On a recent first-semester calculus exam, I gave a bunch of limits. The student was supposed to use L'Hospital's rule if possible, or if not, explain why it didn't work and evaluate it by some other ...
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### How long would it take to teach proper limit calculations?

This question arose from discussion of this question. How long would it take you to teach typical undergratuate (calculus) students the difference between the following two calculations? \lim_{x\...
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### Teaching limits and asymptotics at the same time

Having never been a mathematics educator, my question could be stupid and, if this is the case, please delete it. When I was young, from the very beginning of limits, we were teached that there are ...
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### Should we tell students to never replace parts of an expression by their limits when taking a limit?

Let me explain. Suppose we want to calculate $\lim\limits_{n\to\infty} n^2-n$. Since this limit is indeterminate, one way to do it is to write it as $\lim\limits_{n\to\infty} n^2(1-1/n)$. Since $n^2$ ...
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### Any metaphors/intuitions for a limit of a sequence?

I'm writing (together with a colleague) a minicourse on mathematical analysis (currently we want to cover the Weierstrass theorem on functions on compact intervals, so the aim is to present only the ...
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