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

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

d er i v a t i v e f (x) = e^{8}

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

x \to - \infty lim (\frac{7}{x})

d er i v a t i v e (ln (5 x))^{2}

\int x - \frac{2}{x} d x

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