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

The limit as x approaches-infinity of x-e^x is -infinity

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

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

- \infty

Solution steps

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

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

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

= - \infty - 0

Apply Infinity Property:

- \infty - c = - \infty

= - \infty

\int e^{- x} d x

y = 3 x^{2} + 5 x

\int 64 - x^{2} d x

\frac{d}{d x} (\frac{36}{x ^{2} + 2})

\int - \frac{2 ln ( x )}{x} d x

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