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What does it mean for a function to be bounded on its domain?
Suppose $S$ is an abstract metric space. Suppose $f(x):\Bbb{S} \to \Bbb{R}$. Then how what would the question be asking, if it asks "Show that $f$ is not ...
Apr 17, 2026
Archive: Updates
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Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.
1st: I took the contrapositive. If $a^b$ is irrational, then a and b are irrational. 2nd: I found an example to disprove my contrapositive. Let $a = 2$ Le...
Apr 17, 2026
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indefinite integral of $\cos(x) / x$?
How can I evaluate ; $$\int \frac{\cos(x)}{x} \, dx $$ I tried to do partial integration but it became to an infinite loop of partial integrations
Apr 17, 2026
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Proof of $ |a-b| = |b-a| $
While working out some intriguing qualities of absolute values for my studies of calculus, I frequently used the formula below. I know that the formula be...
Apr 17, 2026
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How to calculate the direction of a curve in a certain point
If you have a curve in parametric form, and you have a point on that curve, how would you calculate the directional vector that has its origin in that poi...
Apr 17, 2026
![Find Magnitude of velocity in a collision? [closed]](https://news.conceivablytech.com/uploads/find-magnitude-of-velocity-in-a-collision-closed_720.jpg)
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Find Magnitude of velocity in a collision? [closed]
A baseball and a ball of clay are approaching each other. The mass of the baseball is $145 \ \mathrm{ g }$ and it is moving due west $5 \ \left.\mathrm{ m...
Apr 17, 2026
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Integration: u-substitution and factoring out constants
I'm struggling solving the following indefinite integral with u-substition. Given: $\int 2\sqrt[]{2x-1} dx , u=2x-1$ I begin to solve by factoring ou...
Apr 17, 2026
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What is the coefficient of $x^3 y^4$ in the expansion of $ (2x-y+5)^8$
I was thinking of doing $\binom{8}{4}$ but not sure if right.
Apr 17, 2026
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User Shogo Makishima - Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields
Apr 17, 2026
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Is there a known mathematical equation to find the nth prime?
I've solved for it making a computer program, but was wondering there was a mathematical equation that you could use to solve for the nth prime?
Apr 17, 2026
