# Tagged Questions

Questions related to memory devices that help learners recall larger pieces of information, especially in the form of lists like characteristics, steps, stages, parts.

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### Are there examples of when the ILATE mnemonic for choosing factors when integrating by parts fails?

Is it possible in some cases that using the ILATE rule does not yield an explicit antiderivative but making another choice does yields one? If so, please give examples.
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### Remembering that $\sin^2(\theta) = 1/2 - 1/2\cos(2\theta)$?

How do you remember this for integrals? It doesn't seem obvious and I can never remember it when I come across it in integrals.
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### What is the good way to remember the signs of the rotational matrix?

Recall rotational matrix in (x,y) is given by: $R = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix}$ For the life of me I cannot remember if the ...
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### How can I remember whether finite or countable cartesian product of countable set is countable

I always forget this result Is cartesian product of countable set countable under finite or countable cartesian products? Is there a good way to remember this? Like a proof sketch where the ...
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### How to remember sum to product and product to sum trigonometric formulas?

They are: I have found nice mnemonics that helped me to remember the reduction formulae and others but I can't find a simple relationship between the formulas above. Can you help?
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### What makes this mnemonic device work for multiplication?

I stumbled across a mnemonic device related to multiplication, outlined on this wikipedia page. I see that it does work, but I'd like to know why. It works as follows (from the wikipedia page): ...
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### Index notation of tensors and mnemonics

I've been trying to learn to manipulate tensors but I've got probably too comfortable with all the matrices in my Linear Algebra course, that it gets really difficult beyond rank-3 tensors. So, ...
Specific question: how can I improve on mentally performing calculations like these : $$(78-59)\times23-8\%\times(270+130)$$ [2\text{digit}+-2\text{digit}]\times2\text{digit}+-x\%\text{of}[3\text{...
The centroid of a region bounded by two curves is given by: $\bar{x} = \frac{1}{A}\int_a^b{x\left[f(x)-g(x)\right]dx}$ \$ \bar{y} = \frac{1}{A}\int_a^b{\left[\frac{(f(x)+g(x)}{2}(f(x)-g(x))\right]...