I don't know how to do related rates with the correct "derivative with respect to time" when the variables are not constant. A girl flies a kite at a...

This may sound like a dumb question, but does $\sin(5x)=5\sin(x)$? Can you say this for any trigonometric function if it is true (e.g. can $\tan^{-1}(7x)=...

This might be more philosophy than math, but it’s been bothering me for a while. Question: If there’s an infinite amount of real numbers between $ 0 $ and...

Recently, I had a look at this question on Quora about how the values of integer tangents from $\tan(1^{\circ})$ to $\tan(90^{\circ})$ sum to $1$. I tried...

I think I have some understanding of what an analytic function is — it is a function that can be approximated by a Taylor power series. But why is the not...

I'm trying to understand the main ideas used in the original proof by Lefschetz of his Hyperplane theorem. Here it is sketched shortly (source: Here)...

I found a question that asked to find the limiting value of $$10\sqrt{10\sqrt{10\sqrt{10\sqrt{10\sqrt{...}}}}}$$If you make the substitution $x=10\sqrt{10...

I first thought to use the Taylor series of $\displaystyle \frac{1}{1+x}$, which makes $$\frac{1}{x^2+2x+2}=\frac{1}{1+(x+1)^2}=1-(x+1)^2+(x+1)^4-\cdots$$...

In everyday life we have a clear notion of what it means for something to be larger than something else. Usually we would evaluate something's size b...

If we consider the equation of a circle, $x^2+y^2=r^2$, then I understand that $dy/dx$ can be computed in the following way via implicit differentiation: ...