What is the limit as x approaches infinity of e 1/x ?

The limit as x approaches infinity of e 1/x is 0

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limit as x approaches infinity of e 1/x

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

0

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= e \cdot x \to \infty lim (\frac{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

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

x \to \infty lim (1) = 1

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

= e \frac{1}{\infty}

Simplify

e \frac{1}{\infty} : 0

= 0

f (x) = 5 x, at x = 1

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x \to 0 lim (x + 1)

\frac{\partial}{\partial z} (\frac{y}{x ^{2} + y ^{2} + z ^{2}})

\frac{d ^{6}}{d x ^{6}} (x^{- 7})

What is the limit as x approaches infinity of e 1/x ?
The limit as x approaches infinity of e 1/x is 0