What is the limit as x approaches 0+of (tan(8x))^x ?

The limit as x approaches 0+of (tan(8x))^x is 1

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limit as x approaches 0+of (tan(8x))^x

x \to 0 + lim ((tan (8 x))^{x})

1

Solution steps

x \to 0 + lim ((tan (8 x))^{x})

Apply exponent rules

= x \to 0 + lim (e^{x l n (t a n (8 x))})

Apply the Limit Chain Rule:

1

= 1

(x^{2} + 1)^{x}

\frac{16}{s ( s ^{2} + 4 s + 16 )}

\frac{1 - y}{x - 1}

\frac{\partial}{\partial x} (1 + y)

What is the limit as x approaches 0+of (tan(8x))^x ?
The limit as x approaches 0+of (tan(8x))^x is 1