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 Notation

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}

\frac{\partial}{\partial x} (56 y^{6} x^{6} - 42 y^{5} x^{5})

\frac{d}{d x} (arcsin (x) + 1 - x^{2})

f (x) = e^{x} - x^{4}

\frac{\partial}{\partial x} (- x e^{x})

n = 1 \sum \infty ln (\frac{n}{2 n + 5})

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