What is the limit as x approaches 0 of (x-5)e^{1/x} ?

The limit as x approaches 0 of (x-5)e^{1/x} is diverges

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limit as x approaches 0 of (x-5)e^{1/x}

x \to 0 lim ((x - 5) e^{\frac{1}{x}})

diverges

Solution steps

x \to 0 lim ((x - 5) 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 - 5) e^{\frac{1}{x}}) = - \infty

x \to 0 - lim ((x - 5) e^{\frac{1}{x}}) = 0

= diverges

x \to \infty lim (4^{2 x})

x \to \infty lim (5 (x))

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

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

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

What is the limit as x approaches 0 of (x-5)e^{1/x} ?
The limit as x approaches 0 of (x-5)e^{1/x} is diverges