What is the limit as x approaches infinity of xe^x+1 ?

The limit as x approaches infinity of xe^x+1 is infinity

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limit as x approaches infinity of xe^x+1

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

\infty

Solution steps

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

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

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

x \to \infty lim (1) = 1

= \infty + 1

Apply Infinity Property:

\infty + c = \infty

= \infty

What is the limit as x approaches infinity of xe^x+1 ?
The limit as x approaches infinity of xe^x+1 is infinity