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}) = \infty

= \infty + \infty

Apply Infinity Property:

\infty + \infty = \infty

= \infty

x \to 2 lim (x + f (x) (x + 2))

x \to 0 + 0 lim (x^{s i n (x)})

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

x \to - 12 lim (x + 12)

x \to 4 lim (\frac{8}{x - 4})

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