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 -infinity

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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}})

- \infty

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

x \to 0 + lim (x - 5) = - 5

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

= (- 5) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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

x \to - 1 lim (2^{1 + l n ∣ x ∣})

x \to 0 lim (cos (x + 1 + 6^{x}))

n \to \infty lim (2 - \frac{1}{n})

x \to 0 + lim (x cos (\frac{π}{x}))

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 -infinity