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

The limit as x approaches+0-of 1/x*+e^{1/x} is -infinity

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

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

- \infty

Solution steps

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

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

With the exception of indeterminate form

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

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

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

= - \infty + 0

Apply Infinity Property:

- \infty + c = - \infty

= - \infty

y = 6 x^{2} e^{x}

\int x^{2} (2 x + \frac{2}{3}) d x

y = (x^{3} - 9 x)^{12}, (- 3, 0)

\int (4 sin (x) + 2 cos (x)) d x

x^{2} (1 - 5 x)

What is the limit as x approaches+0-of 1/x*+e^{1/x} ?
The limit as x approaches+0-of 1/x*+e^{1/x} is -infinity