Questions tagged [limits]
For question regarding the properties and evaluation of limits.
36
questions
13
votes
6
answers
5k
views
"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/...
- 2,039
0
votes
1
answer
176
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 ...
2
votes
2
answers
925
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 ...
- 153
0
votes
2
answers
204
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 ...
- 121
3
votes
6
answers
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 ...
- 425
-2
votes
1
answer
190
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 ...
- 1,152
1
vote
1
answer
217
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 ...
- 229
7
votes
8
answers
5k
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 ...
- 223
1
vote
1
answer
341
views
Limit from both sides or from left? [closed]
Is it possible to write a problem statement as follows:
A function $f$ is defined on $]0,1[$ as $f(x)=x$. Determine $\lim_{x\to 1}f(x)$.
Or should one write always as:
A function $f$ is defined on $]0,...
- 21
6
votes
2
answers
907
views
Calculus limits taught in the US vs Spain?
So, I realize this can be a broad question, so I'll narrow it down. I have lived in Spain and own several Math textbooks from that country (the equivalent of 8th grade and high school Math). Has ...
- 61
3
votes
3
answers
254
views
Differing Choices of $\delta$ in a Limit
In conceptually motivating the $\epsilon-\delta$ definition and proof of a limit, I realized a new way of choosing the $\delta$.
For example, consider $\lim_{x\to 4}\sqrt{x}=2$. In the "standard ...
- 8,039
4
votes
1
answer
199
views
When evaluating the limit of $f(x, y)$ as $(x, y)$ approaches $(x_0, y_0)$, should we consider only those $(x, y)$ in the domain of $f$?
When evaluating the limit of $f(x, y)$ as $(x, y)$ approaches $(x_0, y_0)$, we should or should not consider only those $(x, y)$ in the domain of $f(x, y)$ ? I am confused by different practices of ...
- 51
11
votes
3
answers
660
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 ...
- 379
11
votes
4
answers
536
views
An intuitive explanation of l'Hôpital's rule for ∞/∞
L'Hôpital's rule for the indeterminate form $\frac00$ at finite points can be given a nice intuitive explanation in terms of local linear approximations. See for instance this textbook or this one. ...
- 6,580
4
votes
3
answers
192
views
(use of de L'Hospital's rule) How would you explain this limit to high school students?
Someone asks the following question:
Determine the values for the real numbers $a$ and $b$ such that
$$\lim_{x\to0}\frac{ae^x+b\cos x}{x}=2$$
The students directly apply de LHospital's rule for the ...
- 41