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

The limit as x approaches 3 of (1+x)^{1/x} is 4^{1/3}

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limit as x approaches 3 of (1+x)^{1/x}

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

4^{\frac{1}{3}}

Decimal

1.58740 \dots

Solution steps

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

Plug in the value

x = 3

= (1 + 3)^{\frac{1}{3}}

Simplify

= 4^{\frac{1}{3}}

x \to 3 lim (\frac{cos ^{2} ( x )}{x})

x \to 3 lim (\frac{( 7 ^{x} - 5 ^{x} )}{x})

x \to 3 lim (\frac{3}{x ^{5}})

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

x \to 3 lim (ln (x) ln (1 + x))

What is the limit as x approaches 3 of (1+x)^{1/x} ?
The limit as x approaches 3 of (1+x)^{1/x} is 4^{1/3}