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

x \to - \infty lim (\frac{x}{5})

x \to 3 + lim (\frac{1}{( x - 3 ) ^{5}})

x \to 2 lim (x + 2 - 2)

h \to 0 lim (\frac{( 4 sin ( \frac{π}{2} + h ) - 4 sin ( \frac{π}{2} ) )}{h})

x \to 0 lim (\frac{x ^{2} + 4 x + 5 + 5}{x})

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