What is the limit as x approaches 1+of x^{1/(2x-2)} ?

The limit as x approaches 1+of x^{1/(2x-2)} is sqrt(e)

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limit as x approaches 1+of x^{1/(2x-2)}

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

e

Decimal Notation

1.64872 \dots

Solution steps

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

Apply exponent rules

= x \to 1 + lim (e^{\frac{1}{2 x - 2} l n (x)})

Apply the Limit Chain Rule:

e

= e

x \to 6 - lim (ln (\frac{1}{( 6 - x )}))

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

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

x \to π lim (\frac{- 2}{π - x})

x \to - 6 lim (- x + 2)

What is the limit as x approaches 1+of x^{1/(2x-2)} ?
The limit as x approaches 1+of x^{1/(2x-2)} is sqrt(e)