Let us assume that the zeros of $f = \{Z_1,\ldots,Z_n,a\}$ are infinite and converge towards $a$. The book which I am reading says that any neighborhood o...

I tried to understand the difference between rational numbers and irrational numbers. I understand what is a rational number (a number that can be express...

If a problem asks to find the coefficient of a variable, say, $x^2$, in a large binomial expansion, is there a way to solve without doing the whole expans...

I'm reading Combinatorics and Graph Theory, 2nd Ed., and am beginning to think the terms used in the book might be outdated. Check out the following ...

The Mandelbrot set is defined over the complex numbers and is quite complicated. It's defined by the complex numbers $c$ that remain bounded under th...

Everyone knows the picture that explains instantly the small angle approximation to the sine function (as defined by the parametrisation of the unit circl...

I found the following problem in my calculus book: Solve: $$\lim_{x\to \infty } \left(\frac{\ln (2 x)}{\ln (x)}\right)^{\ln (x)} $$ I tried to solve it us...

Why we take unit circle in trigonometry? If we take circle of radius 2 then how does it mess up with values of trig functions at given angles? thanks

I've been learning the fundamental theorem of calculus. So, I can intuitively grasp that the derivative of the integral of a given function brings yo...

This is not a homework question $\sqrt{i^4} = \sqrt{1} = 1$ $\sqrt{i^4}=i^{\frac{4}{2}}\ =\ i^2=-1$ So what did I do wrong?