What is the limit as x approaches 0-of 2+e^{1/x} ?

The limit as x approaches 0-of 2+e^{1/x} is 2

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limit as x approaches 0-of 2+e^{1/x}

x \to 0 - lim (2 + e^{\frac{1}{x}})

2

Solution steps

x \to 0 - lim (2 + e^{\frac{1}{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 0 - lim (2) + x \to 0 - lim (e^{\frac{1}{x}})

x \to 0 - lim (2) = 2

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

= 2 + 0

Simplify

= 2

x \to 2 lim (1776)

x \to 0 lim (\frac{4 x}{x ^{2} + x})

x \to - 4 lim (x^{2} + 9)

x \to 0 lim (sin (1 - cos (x)))

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

What is the limit as x approaches 0-of 2+e^{1/x} ?
The limit as x approaches 0-of 2+e^{1/x} is 2