What is the limit as x approaches infinity of e^{-x} ?

The limit as x approaches infinity of e^{-x} is 0

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limit as x approaches infinity of e^{-x}

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

0

Solution steps

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

Simplify

e^{- x} : \frac{1}{e ^{x}}

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

x \to \infty lim (1) = 1

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

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

\frac{\partial}{\partial x} (\frac{2 x - 3}{x y})

7 - 3 u

\frac{\partial}{\partial y} (x^{2} y + 3 y + x^{2} y^{3} - 4 x)

y^{^{''}} + y^{^{'}} - 2 y = 2 t, y (0) = 0, y^{^{'}} (0) = 7

y = x^{3} - 2 x + 2 (2.6)

What is the limit as x approaches infinity of e^{-x} ?
The limit as x approaches infinity of e^{-x} is 0