What is the limit as x approaches infinity of (e^{2x})/(e^{2x)+1} ?

The limit as x approaches infinity of (e^{2x})/(e^{2x)+1} is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches infinity of (e^{2x})/(e^{2x)+1}

x \to \infty lim (\frac{e ^{2 x}}{e ^{2 x} + 1})

1

Solution steps

x \to \infty lim (\frac{e ^{2 x}}{e ^{2 x} + 1})

Divide by

e^{2 x} : \frac{1}{1 + \frac{1}{e ^{2 x}}}

= x \to \infty lim (\frac{1}{1 + \frac{1}{e ^{2 x}}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 1 + \frac{1}{e ^{2 x}} )}

x \to \infty lim (1) = 1

x \to \infty lim (1 + \frac{1}{e ^{2 x}}) = 1

= \frac{1}{1}

Simplify

= 1

\int \frac{1}{1 + 21 x} d x

f (x) = e^{8}

\int cos (x) - sin (x) d x

y = 1 - x^{4}, y = 0

\frac{\partial}{\partial y} ((x e^{y})^{2})

What is the limit as x approaches infinity of (e^{2x})/(e^{2x)+1} ?
The limit as x approaches infinity of (e^{2x})/(e^{2x)+1} is 1