What is the limit as x approaches 0+of 3(tan(x))^x ?

The limit as x approaches 0+of 3(tan(x))^x is 3

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limit as x approaches 0+of 3(tan(x))^x

x \to 0 + lim (3 (tan (x))^{x})

3

Solution steps

x \to 0 + lim (3 (tan (x))^{x})

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

= 3 \cdot x \to 0 + lim ((tan (x))^{x})

Apply exponent rules

= 3 \cdot x \to 0 + lim (e^{x l n (t a n (x))})

Apply the Limit Chain Rule:

1

= 3 \cdot 1

Simplify

= 3

x \to 0 lim (\frac{4 x - 2 x ^{2}}{sin ( x )})

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

x \to + 0 + lim (sin (x) n x)

n \to 1 lim (\frac{n ^{3} - 1}{n - 1})

x \to 0 lim (\frac{x ^{2} - 2 x}{3 x})

What is the limit as x approaches 0+of 3(tan(x))^x ?
The limit as x approaches 0+of 3(tan(x))^x is 3