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

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

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

= diverges

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