What is the limit as x approaches 0+of (tan(5x))^x ?

The limit as x approaches 0+of (tan(5x))^x is 1

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limit as x approaches 0+of (tan(5x))^x

x \to 0 + lim ((tan (5 x))^{x})

1

Solution steps

x \to 0 + lim ((tan (5 x))^{x})

Apply exponent rules

= x \to 0 + lim (e^{x l n (t a n (5 x))})

Apply the Limit Chain Rule:

1

= 1

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What is the limit as x approaches 0+of (tan(5x))^x ?
The limit as x approaches 0+of (tan(5x))^x is 1