# Questions tagged [calculus]

For questions applying to calculus courses. Topics include derivatives, integrals, limits, continuity, series, application questions, etc.

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### Any examples of calculus sequence that deemphasizes calculation tricks?

I'm considering creating a series of classes that explore deeper ideas in calculus without overemphasizing the various computational tricks used in integration and differentiation. My vision is ...
2k views

### How can we explain intuitively the convergence and divergence of these two series?

It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
259 views

### Is this a viable Calculus 1 question?

A person is standing next to a hot air balloon. At the same time, the person starts moving away from the balloon at 5 ft/sec and the balloon rises straight into the air at a rate of 12 ft/sec. Is the ...
15k views

### Why not think of derivatives as fractions?

Back in high school—back in the 1900s, as my sons say—when our calculus teacher was introducing the chain rule... $\frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx}$ ...he made a special point of ...
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/...
7k views

### Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

Background I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to ...
1 vote
212 views

### What would be a good pacing for teaching this calculus 2 course?

Next semester I'm going to lecture calculus 2 in an institution I just joined. However, when I had calculus 2 back then the syllabus was very different, it mainly covered several variable calculus up ...
1 vote
133 views

### Sourcing and verifying calculus applications

There are many questions on this site about specific (or not-so-specific) applications of calculus to the "real world". However, one issue I've noticed in using textbooks for this purpose ...
1 vote
261 views

### Is there any university or college in any country where failure and dropout rates in Calculus are not so high?

Calculus is a foundational mathematics course that is often seen as a bottleneck for STEM majors. However, it is also a course that is notorious for its high dropout rates. In the United States, for ...
3k views

### How to properly define volume for beginner calculus students?

I'm interested in opinions based on experience about how to introduce volume for beginner calculus students. Below I present some observations and specific questions. In Stewart's book, the volume of ...
2k views

### How to explain that integral calculate areas?

I teach internal combustion engines theory in a technical school. I have an elementary knowledge of calculus and my students lack even this. I want to intuitively explain them what is the pdV integral,...
1 vote
209 views

### Calculus at competitive level or Olympiad level

What are the topics of Calculus which can be useful for competitive level and the students are not exposed to it ?