Newbetuts

Is it valid to write $1 = \lim_{x \rightarrow 0} \frac{e^x-1}{x} = \frac{\lim_{x \rightarrow 0} (e^x) -1}{\lim_{x \rightarrow 0} x}$?

Show $\sum_{k=1}^\infty \frac{k^2}{k!} = 2\mathrm{e}$ [duplicate]

Prove that $e>2$ geometrically.

How many different definitions of $e$ are there?

How does calculus without Euler's number (e) look? [closed]

How to find the value of an unknown exponent?

Asymptotic to a sequence of algebraic numbers.

relationship between doubling time and growth rate

How can you show by hand that $ e^{-1/e} < \ln(2) $?

Definition of exponential function, single-valued or multi-valued?

Rational series representation of $e^\pi$

How to prove that $\lim_{h\to 0} \, \frac{e^h-1}{h}$

A binomial inequality with factorial fractions: $\left(1+\frac{1}{n}\right)^n<\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+...+\frac{1}{n!}$

Finding asymptotes of exponential function and one-sided limit

Find the smallest k such that $n^k > \sum_{i=0}^{n-1} i^k$

Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$ [duplicate]

Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$

New posts in exponential-function

Solving $4x = e^x$ without graphing and looking for intersection

What is the name of the answer to exponentiation?

Is the natural logarithm actually unique as a multiplier?

Is it valid to write $1 = \lim_{x \rightarrow 0} \frac{e^x-1}{x} = \frac{\lim_{x \rightarrow 0} (e^x) -1}{\lim_{x \rightarrow 0} x}$?

Show $\sum_{k=1}^\infty \frac{k^2}{k!} = 2\mathrm{e}$ [duplicate]

Prove that $e>2$ geometrically.

How many different definitions of $e$ are there?

How does calculus without Euler's number (e) look? [closed]

How to find the value of an unknown exponent?

Asymptotic to a sequence of algebraic numbers.

relationship between doubling time and growth rate

How can you show by hand that $ e^{-1/e} < \ln(2) $?

Definition of exponential function, single-valued or multi-valued?

Rational series representation of $e^\pi$

How to prove that $\lim_{h\to 0} \, \frac{e^h-1}{h}$

A binomial inequality with factorial fractions: $\left(1+\frac{1}{n}\right)^n<\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+...+\frac{1}{n!}$

Finding asymptotes of exponential function and one-sided limit

Find the smallest k such that $n^k > \sum_{i=0}^{n-1} i^k$

Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$ [duplicate]

Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$