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 diverges

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

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

diverges

Solution steps

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

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

= diverges

x \to 0 lim (cos (x) sec (x))

x \to 4 + lim (3 x^{2} - 9)

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

x \to 3 lim (ln (e^{3 x}))

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

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 diverges