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

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

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

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

e^{\frac{1}{e}}

Decimal Notation

1.44466 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e^{\frac{1}{e}}

= e^{\frac{1}{e}}

y^{^{''}} + 9 y = e^{t} (cos (3 t) + sin (3 t))

x \to 9 lim (7 x + ∣ x - 9 ∣)

f (x) = \frac{x ^{3}}{4} - 3 x

\frac{\partial}{\partial x} (y^{3} cos (3 x) \cdot 3)

\frac{d}{d x} (e^{x} + e^{- x} - 2)

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