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

The limit as x approaches infinity of e^{-x}-ln(x) is -infinity

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limit as x approaches infinity of e^{-x}-ln(x)

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

- \infty

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

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

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

= 0 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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