Find the derivative of $y=\sin^2(3x)$
Our instructor had given us an equation and we should get the derivative of it. But even him, he is confused what to do (funny college instructor) if we s...
Apr 11, 2026 1 VIEWS
Topic: General
5104 Articles 
Is there a rigorous definition of a line?
In the sources I can find, line is considered a primitive concept (a one without definition). There is something, however, in such an intuitive definition...
Apr 11, 2026 1 VIEWS
What is the difference between implication symbols: $\rightarrow$ and $\Rightarrow$? [duplicate]
I do not understand the difference between $\rightarrow$ and $\Rightarrow$. Sometimes I see implication truth tables labeled with the former, sometimes wi...
Apr 11, 2026 1 VIEWS
Laplace transform of $1/t$
Does the laplace transform of $1/t$ exist? If yes, how do we calculate it? Putting it in $$\int_0^\infty (e^{-st}/t) dt$$ won't solve. Is there any o...
Apr 11, 2026 1 VIEWS
Can skew lines be perpendicular?
In a math textbook for primary school, there's a picture like the one below. They explain which of the line segments are perpendicular and which are ...
Apr 11, 2026 1 VIEWS
What does it mean to solve a system of linear equations simultaneously?
A system of linear equations is a finite collection of linear equations that is to be solved simultaneously. Does the phrase 'solving the system simu...
Apr 11, 2026 2 VIEWS
How do I tell if this function is a probability density function?
If I have $$f(x)=\sin(x\pi/10)\qquad\text{for}\;0\leq x\leq10.$$ How do I tell if it is a probability density function? And if it isn't how do I norm...
Apr 11, 2026 1 VIEWS
Cauchy-Riemann equations in polar form. [duplicate]
Show that in polar coordinates, the Cauchy-Riemann equations take the form $\dfrac{\partial u}{\partial r} = \dfrac{1}r \dfrac{\partial v}{\partial \theta...
Apr 11, 2026 3 VIEWS
What is a 0-ball?
I'm reading a paper that says $\bigcap V_{T,X}$ is either empty or a closed $l$-ball where $T \subset S$ is a subset of points $S$ and $\operatorname...
Apr 11, 2026 1 VIEWS
The greatest area for a rectangle on a track field.
An athletic field with a perimeter of 0.25 miles consists of a rectangle with a semicircle at each end, as shown below. Find the dimensions that yield the...
Apr 11, 2026 1 VIEWS
Finding Maxima and Minima Values when the second derivative is a constant
I am given the following quadratic over the closed interval $[0,3]$ $f(x) = x-x^2$ I'm asked to find the value inside that interval that is the large...
Apr 11, 2026 1 VIEWS
If I have three points, is there an easy way to tell if they are collinear? [duplicate]
Points $(a,b)$, $(m,n)$, and $(x,y)$ are selected at random. What is the quickest/easiest way to tell if they are collinear? At first I thought it was a m...
Apr 11, 2026 1 VIEWS