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

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

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

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

1

Solution steps

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

Simplify

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

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

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

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

= 1 \cdot 1

Simplify

= 1

x \to 2 lim (4 x^{2} - x + 5)

x \to 0 + lim ((1 + 5 x)^{\frac{3}{x}})

x \to 4 lim (2 x^{2} - 3 x + 40)

x \to 1 lim (3 x^{2} - 5 x + 2)

x \to 2 lim (lo g_{2} (x + 2))

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