What is the limit as x approaches 0+of (tan(4x))^x ?

The limit as x approaches 0+of (tan(4x))^x is 1

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limit as x approaches 0+of (tan(4x))^x

x \to 0 + lim ((tan (4 x))^{x})

1

Solution steps

x \to 0 + lim ((tan (4 x))^{x})

Apply exponent rules

= x \to 0 + lim (e^{x l n (t a n (4 x))})

Apply the Limit Chain Rule:

1

= 1

\frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

\int - x^{7} \cdot e^{x^{8} - 7} - 2 x d x

\int 14 x e^{7 x} d x

x \to 3 lim (\frac{3}{x ^{2} - 9})

f (θ) = 4 tan (θ)

What is the limit as x approaches 0+of (tan(4x))^x ?
The limit as x approaches 0+of (tan(4x))^x is 1