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

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

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

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

1

Solution steps

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

x \to 0 - lim (1) = 1

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

= 1 + 0

Simplify

= 1

3 t^{2} + 15 t + 15

y = (5 x^{2} - 1)^{- 3}

\int_{- \infty}^{0} x e^{8 x} d x

2 x^{2} - 4 x

\frac{\partial}{\partial z} (- z)

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