What is the limit as x approaches 0+of 2(tan(x))^x ?

The limit as x approaches 0+of 2(tan(x))^x is 2

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limit as x approaches 0+of 2(tan(x))^x

x \to 0 + lim (2 (tan (x))^{x})

2

Solution steps

x \to 0 + lim (2 (tan (x))^{x})

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

= 2 \cdot x \to 0 + lim ((tan (x))^{x})

Apply exponent rules

= 2 \cdot x \to 0 + lim (e^{x l n (t a n (x))})

Apply the Limit Chain Rule:

1

= 2 \cdot 1

Simplify

= 2

\frac{d y}{d x} = \frac{( x ^{2} + y ^{2} )}{2 x y}

y^{^{''}} - y = \frac{e ^{x}}{e ^{x} + 1}

\frac{d}{d x} (ln (\frac{x + 1}{x - 2}))

\int_{1}^{\infty} \frac{5}{x ^{4}} d x

\int (2 - x) d x

What is the limit as x approaches 0+of 2(tan(x))^x ?
The limit as x approaches 0+of 2(tan(x))^x is 2