What is $\dfrac{dr}{d\theta}$?
Suppose we have an equation of a polar curve with usual notation $r=f(\theta).$ I am curious about the geometric meaning of $$\dfrac{dr}{d\theta}=f'(...
Apr 13, 2026 1 VIEWS
Topic: General
5104 Articles 
What are the best texts on undergraduate linear algebra?
I have recently finished a course in 'elementary linear algebra,' which entails basic systems of linear equations, in-depth study on matrices, t...
Apr 13, 2026 1 VIEWS
How to find $ P $ such that $ A^\top = PAP^{-1} $?
Let $ A $ be a matrix such that $A \in \operatorname{Mat}_3(\mathbb{R}) $. How to find $ P \in \operatorname{Mat}_3(\mathbb{R}) $, without doing heavy cal...
Apr 13, 2026 1 VIEWS
What does the $t$ in $(x,y,z)^t$ mean?
Just a question on notation. I have seen a plane defined this way: $$S = \{(x,y,z)^t \in \mathbb{R}^3 \ / \ 2x-3y+z = 0\}$$ See the $t$ superscript on $(x...
Apr 13, 2026 1 VIEWS
Negative limit answer
Find $\lim_{x\to 13} {5x-65 \over 169-x^2}.$ My answer is $5 \over 26$. Symbolab and WolfRam answer $-{5 \over 26}$. Where does the negative come from?
Apr 13, 2026 1 VIEWS
Find the Area of the ellipse
Given $$\frac{x^2}{a^2} + \frac{y^2}{b^2}=1$$ where $a>0$, $b>0$ I tried to make $y$ the subject from the equation of the ellipse and integrate from...
Apr 13, 2026 1 VIEWS
How to solve a system of two equations in three unknowns
$x+y=5$ $2x+y-3z=12$ I know that in order to solve three unknowns three equations are needed, so I'm unsure if this can be solved or if different tec...
Apr 13, 2026 1 VIEWS
Division with negative exponents
I have a problem that looks like this: $$\frac{20x^5y^3}{5x^2y^{-4}}$$ Now they said that the "rule" is that when dividing exponents, you bring them on to...
Apr 13, 2026 2 VIEWS
Subtraction of a negative number
Why subtraction of a negative number from a positive number is addition? Eg: $a - (-b) = a + b$ When looking through the number scale I am unable to relat...
Apr 13, 2026 1 VIEWS
Understanding the integrating factor
I'm trying to understand solving ordinary linear differential equations by using integrating factor. I dont have my book yet so I'm reading from...
Apr 13, 2026 1 VIEWS
GRE exam word problem: show that a higher percentage of total agricultural acreage was fallow in United States than in the Soviet Union.
A ten year comparison between the United States and the Soviet Union in terms of crop yields per acre revealed that when only planted acreage is compared,...
Apr 13, 2026 1 VIEWS
What does the supremum of a sequence of sets represent?
I'm trying to understand more about the limits of sequences of sets in Measure Theory. Given a sequence of sets $\{A_n\}_{n\in \mathbb{N}} = \{ A_1,A...
Apr 13, 2026 1 VIEWS