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

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

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

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

e

Decimal Notation

2.71828 \dots

Solution steps

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

Apply exponent rules

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

e^{\frac{1}{l n ( x )} l n (x)} = e

= x \to 1 + lim (e)

x \to a lim c = c

= e

x \to 0 lim (sin (x))

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

z \to 0 lim ((cos (z))^{\frac{1}{z ^{2}}})

x \to \infty lim (\frac{( 2 sin ( 3 x ) )}{5 x})

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

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