Is there a rule of integration that corresponds to the quotient rule?
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Is there a rule of integration that corresponds to the quotient rule?

When teaching the integration method of u-substitution, I like to emphasize its connection with the chain rule of integration. Likewise, the intimate conn...

Published: Aug 10, 2026

When an equation has no solutions, denote it with $x\in\varnothing$.
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When an equation has no solutions, denote it with $x\in\varnothing$.

My teacher claims that when an equation in variables $x_1,x_2,\ldots,x_n$ has no solutions, you should denote this fact with $(x_1,x_2,\ldots,x_n)\in\varn...

Published: Aug 10, 2026

Probability of Head in coin flip when coin is flipped two times
general

Probability of Head in coin flip when coin is flipped two times

Probability of getting a head in coin flip is $1/2$. If the coin is flipped two times what is the probability of getting a head in either of those attempt...

Published: Aug 10, 2026

What is a particular and a homogenous solution of a differential equation?
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What is a particular and a homogenous solution of a differential equation?

When solving linear nonhomogeneous equations, we deal with two types of solutions: particular homogeneous Why do we have these two types of solutions for ...

Published: Aug 10, 2026

Sum of Fibonacci numbers
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Sum of Fibonacci numbers

While trying to find find a formula to calculate the length of the golden spiral I came across the sum of the Fibonacci numbers. I noticed that $$\text{Fi...

Published: Aug 10, 2026

Linear combination of x
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Linear combination of x

Is $3x + 4x^2 + y$ a valid linear combination of $x$? I'm not sure if "a linear combination of $x$" allows for other terms than $x$ which would just ...

Published: Aug 10, 2026

How many different possible Wordle tweets can exist?
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How many different possible Wordle tweets can exist?

Wordle is a viral web game where you have up to six attempts to guess a secret five-letter English word* using the letters A-Z. After each $5$-letter gues...

Published: Aug 10, 2026

Is there a valid,
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Is there a valid, "shortcut" method to convert a quadratic from vertex form to factored form?

Recently, I had a couple of students give me an interesting way of converting from vertex form to factored form that I've never seen before. One told...

Published: Aug 10, 2026

how to find derivative of $x^2\sin(x)$ using only the limit definition of a derivative
updates

how to find derivative of $x^2\sin(x)$ using only the limit definition of a derivative

I'm trying to find the derivative of $x^2\sin x$ using only the limit definition of a derivative. I've tried two approaches, one using the diffe...

Published: Aug 10, 2026

Minimal axioms for a group
general

Minimal axioms for a group

My group theory is very rusty. If I want to just start with left inverses and left identities, must I link the axioms, or can I leave them independent? e....

Published: Aug 10, 2026

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