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

The limit as x approaches infinity of (e^{1-x})/(1+x) is 0

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

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

0

Solution steps

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

x \to \infty lim (e^{1 - x}) = 0

x \to \infty lim (1 + x) = \infty

= \frac{0}{\infty}

Apply Infinity Property:

\frac{0}{\infty} = 0

= 0

What is the limit as x approaches infinity of (e^{1-x})/(1+x) ?
The limit as x approaches infinity of (e^{1-x})/(1+x) is 0