What is the limit as x approaches-infinity of (4e^{1/x}-1)/(1+e^x) ?

The limit as x approaches-infinity of (4e^{1/x}-1)/(1+e^x) is 3

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limit as x approaches-infinity of (4e^{1/x}-1)/(1+e^x)

x \to - \infty lim (\frac{4 e ^{\frac{1}{x}} - 1}{1 + e ^{x}})

3

Solution steps

x \to - \infty lim (\frac{4 e ^{\frac{1}{x}} - 1}{1 + e ^{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} ( 4 e ^{\frac{1}{x}} - 1 )}{lim _{x \to - \infty} ( 1 + e ^{x} )}

x \to - \infty lim (4 e^{\frac{1}{x}} - 1) = 3

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

= \frac{3}{1}

Simplify

= 3

y = cos (x) sin (x)

\int \frac{2}{x ^{2} - 3 x + 2} d x

\frac{\partial}{\partial x} (cos (x + 8 y))

\int_{0}^{l n (2)} \frac{e ^{3 x}}{1 + e ^{6 x}} d x

What is the limit as x approaches-infinity of (4e^{1/x}-1)/(1+e^x) ?
The limit as x approaches-infinity of (4e^{1/x}-1)/(1+e^x) is 3