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/...
581 views

Terminology for parts of limit notation

When we talk about: $$\lim_{x\to{c}}f(x)=L.$$ Is there a formal name for the number "$c$"? I know that the notation means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It ...
171 views

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 ...
187 views

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 ...
1k views

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 ...
164 views

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 ...
2k views

What is the intuition behind the limit superior?

I want to write an article which explains the limit superior. I also want to present the intuition behind this concept. Currently I would describe the limit superior as the "least upper bound of a ...
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 ...
451 views

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 ...
1 vote
197 views

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 ...
4k views

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 ...
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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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\...