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Limit of $\frac{x^y-y^x}{x^x-y^y} $ while $x\to y$
calculus
limits
exponential-function
Prove $\lim\limits_{n\to∞}{\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-(x+1)})^{n+1}\over\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-x})^{n + 1}}=\frac 13$
limits
exponential-function
binomial-coefficients
Find $x$ from $3^x\cdot x^3 = 1$
logarithms
exponential-function
Why is $ \sum_{n=0}^{\infty}\frac{x^n}{n!} = e^x$?
sequences-and-series
algebra-precalculus
power-series
exponential-function
How to show $\frac{19}{7}<e$
inequality
summation
exponential-function
Eigenvector and eigenvalue for exponential matrix
abstract-algebra
matrices
eigenvalues-eigenvectors
exponential-function
diagonalization
Proof of inequality $e^x + e^{-x} \leq 2e^{x^2}$
algebra-precalculus
inequality
exponential-function
Smallest Possible Power
algebra-precalculus
elementary-number-theory
inequality
logarithms
exponential-function
Can anyone help me with a graph: exponential but never reaches 1
exponential-function
A "relative" of the exponential function
power-series
exponential-function
special-functions
volume
How was $e$ first calculated?
reference-request
soft-question
math-history
exponential-function
Integral Involving Gaussian Q function and exponential
integration
exponential-function
gaussian-integral
Can $\lim_{h\to 0}\frac{b^h - 1}{h}$ be solved without circular reasoning?
calculus
limits
logarithms
exponential-function
alternative-proof
Proof that $e^x$ is a transcendental function of $x$?
exponential-function
transcendental-numbers
domain of $x^x$
exponential-function
How do pocket calculators calculate exponents?
exponential-function
exponentiation
calculator
What are your favorite relations between e and pi? [closed]
soft-question
exponential-function
big-list
pi
Is there a (deep) relationship between these various applications of the exponential function?
probability-theory
exponential-function
lie-groups
fourier-series
lie-algebras
How can we describe the graph of $x^x$ for negative values?
real-analysis
complex-analysis
graphing-functions
exponential-function
Reason for LCM of all numbers from 1 .. n equals roughly $e^n$
number-theory
exponential-function
least-common-multiple
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