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

The limit as x approaches 0+of (tan(3x))^x is 1

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limit as x approaches 0+of (tan(3x))^x

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

y = e^{5 x}, y = e^{6 x}, x = 1

\frac{d}{d x} (2 x y^{3})

x^{3} - 10 x^{2} + 16 x, - x^{3} + 10 x^{2} - 16 x

n = 0 \sum \infty \frac{1}{2 ^{n}}

\frac{d}{d x} ((x^{2} - 5 x + 3) (4 x^{3} + 10 x - 5))

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