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Results tagged with calculus
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user 2049
For questions applying to calculus courses. Topics include derivatives, integrals, limits, continuity, series, application questions, etc.
3
votes
What is the best way to intuitively explain the relationship between the derivative and the ...
Intuitively, the fundamental theorem of calculus states that "the total change is the sum of all the little changes". $f'(x) dx$ is a tiny change in the value of $f$. …
- 1,017
10
votes
2
answers
372
views
What are some good or neat examples of computing a function's Taylor series?
Starting from
\begin{equation*}
\frac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots,
\end{equation*}
which holds when $|x| < 1$,
we can conclude that
\begin{equation*}
\frac{1}{1 + x^2} = 1 - x^2 + x^4 - x^6 + …
- 1,017
23
votes
13
answers
1k
views
Historical tidbits to liven up calculus classes
What are your favorite math history stories to tell when teaching calculus? … Are there any historical math problems, such as the Brachistochrone problem, that could be incorporated into a calculus class? …
- 1,017
1
vote
List of realistic extremum problems
Many important machine learning algorithms, such as training a neural network, require solving a large optimization problem (essentially tuning the neural network weights to minimize the classificatio …
- 1,017