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

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

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

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

diverges

Solution steps

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

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

= diverges

x = y (y - 13), x = - y (y - 13)

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2}})

\frac{d}{d x} (e^{x} sin (x) + cos (x) e^{x})

\frac{d}{d x} (\frac{- 6 x}{( x ^{2} - 4 ) ^{2}})

\int e^{x^{0.5}} d x

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