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 infinity

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

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

\infty

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}}) = \infty

= 1 + \infty

Apply Infinity Property:

c + \infty = \infty

= \infty

x \to 1 lim (∣ 2 x - 2 ∣)

x \to 1 - lim (\frac{4}{x ^{2} - 2 x + 1})

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

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

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

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 infinity