What is the limit as x approaches 0 of 1/(xe^x) ?

The limit as x approaches 0 of 1/(xe^x) is diverges

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limit as x approaches 0 of 1/(xe^x)

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

diverges

Solution steps

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

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

= diverges

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

x \to - 3 lim (\frac{2 x}{x + 5})

x \to 0 + lim (2 x ln (sin (x)))

x \to 3 lim (sin (x - 3))

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

What is the limit as x approaches 0 of 1/(xe^x) ?
The limit as x approaches 0 of 1/(xe^x) is diverges