What is the limit as x approaches 0+of ln((x+1)^x) ?

The limit as x approaches 0+of ln((x+1)^x) is 0

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limit as x approaches 0+of ln((x+1)^x)

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

0

Solution steps

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

Plug in the value

x = 0

= ln ((0 + 1)^{0})

Simplify

ln ((0 + 1)^{0}) : 0

= 0

x \to 1 + lim (ln (x) ln (x - 1))

x \to 4 lim (3 (x - 4)^{x - 4})

x \to - 3 - lim (\frac{4 - x ^{2}}{x + 3})

x \to 0 lim (2 x csc (x))

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

What is the limit as x approaches 0+of ln((x+1)^x) ?
The limit as x approaches 0+of ln((x+1)^x) is 0