What is the limit as x approaches 0-of xe^{1/x}+1 ?

The limit as x approaches 0-of xe^{1/x}+1 is 1

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limit as x approaches 0-of xe^{1/x}+1

x \to 0 - lim (x e^{\frac{1}{x}} + 1)

1

Solution steps

x \to 0 - lim (x e^{\frac{1}{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 0 - lim (x e^{\frac{1}{x}}) + x \to 0 - lim (1)

x \to 0 - lim (x e^{\frac{1}{x}}) = 0

x \to 0 - lim (1) = 1

= 0 + 1

Simplify

= 1

What is the limit as x approaches 0-of xe^{1/x}+1 ?
The limit as x approaches 0-of xe^{1/x}+1 is 1