Jun 23, 2015 · I am proving $(x^n)'=nx^{n-1}$ by the definition of the derivative: \\begin{align} (x^n)'&=\\lim_{h \\to 0} {(x+h)^n-x^n\\over h}\\\\ &=\\lim_{h \\to 0} {x^n ...

How would I go about solving equations of this form: $$ x^x = n $$ for values of n that do not have obvious solutions through factoring, such as $27$ ($3^3$) or $256$ ($4^4$). For instance, how ...

I would like to know: How come that $$\\sum_{n=1}^\\infty n x^n=\\frac{x}{(x-1)^2}$$ Why isn't it infinity?

Aug 17, 2014 · Prove it for n=1; then, assuming that it is true for n=k, try to show that it is true for n=k+1. It is easy indeed. (I do not know the name of this proving method.)

Feb 7, 2020 · Trying x =2 is more more fruitfull, a little checking and guessing gives x = 2 and y =4 a soloution to this, there are also no other y for x=2 as our f is strictly decreasing beyond e. Thus the …

Apr 1, 2017 · In other words, the sequence of functions $\ {\,f_n\}_ {n=1}^\infty$ is normal in $ [0,1)$. I think knowing some Italians would be a good thing to have to your avail at this point.

It should be possible to prove this using the basic properties of numbers discussed in Spivak's book: Associative law for addition, Existence of an additive identify, Existence of additive inverses, …

Prove that $a_n=x^n/n! \to 0$ for all $x$ Here is what I tried, but it seems to lead to nowhere. Choose $\epsilon > 0$. We need to show that there exists $N\in \mathbb {N}$ such that for all $...

Oct 10, 2013 · Can someone please explain why $(x^n)'=n\\cdot x^{n-1}$? Sorry for not writing it in math characters, I'm new here.

Sep 2, 2019 · Seen in martycohen's answer to How to prove that $\frac {\text {d}} {\text {d}x} x^n = nx^ {n-1}$ without using the Binomial Theorem?.