New posts in exponential-function

Limit of $\frac{x^y-y^x}{x^x-y^y} $ while $x\to y$

Prove $\lim\limits_{n\to∞}{\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-(x+1)})^{n+1}\over\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-x})^{n + 1}}=\frac 13$

Find $x$ from $3^x\cdot x^3 = 1$

Why is $ \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$?

How to show $\frac{19}{7}<e$

Eigenvector and eigenvalue for exponential matrix

Proof of inequality $e^x + e^{-x} \leq 2e^{x^2}$

Smallest Possible Power

Can anyone help me with a graph: exponential but never reaches 1

A "relative" of the exponential function

How was $e$ first calculated?

Integral Involving Gaussian Q function and exponential

Can $\lim_{h\to 0}\frac{b^h - 1}{h}$ be solved without circular reasoning?

Proof that $e^x$ is a transcendental function of $x$?

domain of $x^x$

How do pocket calculators calculate exponents?

What are your favorite relations between e and pi? [closed]

Is there a (deep) relationship between these various applications of the exponential function?

How can we describe the graph of $x^x$ for negative values?

Reason for LCM of all numbers from 1 .. n equals roughly $e^n$