What is the limit as x approaches 3 of x^{1/x} ?

The limit as x approaches 3 of x^{1/x} is cube root of 3

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limit as x approaches 3 of x^{1/x}

x \to 3 lim (x^{\frac{1}{x}})

Decimal Notation

1.44224 \dots

Solution steps

x \to 3 lim (x^{\frac{1}{x}})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 3 - lim (x^{\frac{1}{x}}) = 3^{\frac{1}{3}}

x \to 2 lim (81)

h \to 0 lim (∣ h ∣)

x \to 0 lim (\frac{x cos ( 5 x )}{sin ( 5 x )})

x \to \frac{π}{2} lim (x tan (x))

x \to 0 lim (3 \frac{x}{sin ( x )})

What is the limit as x approaches 3 of x^{1/x} ?
The limit as x approaches 3 of x^{1/x} is cube root of 3