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

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

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

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

diverges

Solution steps

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

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

then the limit does not exist

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

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

= diverges

y = arctan (2 t)

\frac{\partial}{\partial x} (2 x^{2} y^{4})

\int cos^{4} (2 x) d x

7 arctan (x + 1 + x^{2})

\frac{\partial}{\partial x} (x y (18 - x - y))

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