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

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

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

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

0

Solution steps

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

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

then

x \to a lim f (x) = L

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

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

= 0

x \to 0 lim (3 (\frac{x}{sin ( x )}))

x \to π - lim (\frac{cos ( x )}{x})

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

n \to \infty lim (n a^{n})

x \to - 4 lim (x^{2} - 3 x + 12)

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