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

t y^{^{'}} + y = t^{3}, y (1) = - 2

\int_{\frac{1}{2}}^{1} (x^{- 3} - 3) d x

x \to 2 lim (x^{3} + 2 x^{2} + 1)

\frac{d y}{d x}, x^{3} - 3 x y^{2} + y^{3} = 1

y^{^{'}} = 3 x + y, y (0) = 5

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