What is the limit as x approaches 0+of (1+tan(x))^{3/x} ?

The limit as x approaches 0+of (1+tan(x))^{3/x} is e^3

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limit as x approaches 0+of (1+tan(x))^{3/x}

x \to 0 + lim ((1 + tan (x))^{\frac{3}{x}})

e^{3}

Decimal

20.08553 \dots

Solution steps

x \to 0 + lim ((1 + tan (x))^{\frac{3}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{3}{x} l n (1 + t a n (x))})

Apply the Limit Chain Rule:

e^{3}

= e^{3}

What is the limit as x approaches 0+of (1+tan(x))^{3/x} ?
The limit as x approaches 0+of (1+tan(x))^{3/x} is e^3