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

x \to - 1 lim (x^{2} + 2 x + 4)

x \to - 2 lim (2 e^{x + 2} - 3)

x \to 0 + lim (\frac{4}{x} - ln (x))

x \to \infty lim ((2^{x} + x)^{\frac{1}{x}})

x \to \infty lim (9 + \frac{1}{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