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

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

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limit as x approaches 0 of ((tan(2x)))/x

x \to 0 lim (\frac{( tan ( 2 x ) )}{x})

2

Solution steps

x \to 0 lim (\frac{tan ( 2 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 2 x ) \cdot 2}{1})

= x \to 0 lim (\frac{sec ^{2} ( 2 x ) \cdot 2}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{sec ^{2} ( 2 \cdot 0 ) \cdot 2}{1} : 2

= 2

7 x + 1

\frac{d}{d x} (6 arcsinh (tan (x)))

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

x \to 7 lim (\frac{9 x}{x - 7})

\frac{d y}{d x} = e^{- x} - y

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