This is a homework question from a precalculus class that I'm a TA for. Let $f$ be the function given by $$ \tag{$\star$} f(x) = \frac{3x-1}{x+2} \,....

I am a Physics undergrad, and just started studying Topology. How do you define neighborhood and open set in Topology.Wikipedia gives a circular definitio...

How can I find $p$ and $q$ in $x^2+px+q = 0$ Knowing only one complex root, for example $2-i$?

So what happens if we multiply infinite number by. Infinitesimal number? Like $dx \times \infty$ where $dx$ is treated as in one-dimensional integration. ...

I know that in problems dealing with rates of change that implicit differentiation is used, however how does this compare to just "regular" differentiatio...

I have two questions about using modulation in equations. My first question is what notation is the right to use (i.e. x%y or mod(x, y))? The second is wh...

Excuse me can you see this question Show that every seconed countable space is separable and first countable I tried on it but i am not sure , I get / Let...

I am studying Linear Algebra, I have 3 questions in my mind What does an inverse matrix mean. I am trying to have a meaning of it, but I don't really...

I've got stuck at this problem : Prove that for any $a > 0$ and any $b > 0$ the following inequality is true: $$ {3} {\left(\frac{a^3}{b^3} + \...

I'm trying to understand the proof of Rank–nullity theorem,but there are parts that I don't understand: Steinitz exchange lemma If ${\displaysty...