What is the limit as x approaches 0+of (15tan(x))^x ?

The limit as x approaches 0+of (15tan(x))^x is 1

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limit as x approaches 0+of (15tan(x))^x

x \to 0 + lim ((15 tan (x))^{x})

1

Solution steps

x \to 0 + lim ((15 tan (x))^{x})

Simplify

(15 tan (x))^{x} : 1 5^{x} tan^{x} (x)

= x \to 0 + lim (1 5^{x} tan^{x} (x))

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 + lim (1 5^{x}) \cdot x \to 0 + lim (tan^{x} (x))

x \to 0 + lim (1 5^{x}) = 1

x \to 0 + lim (tan^{x} (x)) = 1

= 1 \cdot 1

Simplify

= 1

What is the limit as x approaches 0+of (15tan(x))^x ?
The limit as x approaches 0+of (15tan(x))^x is 1