What is the limit as x approaches 0 of (tan(4x))/(2x) ?

The limit as x approaches 0 of (tan(4x))/(2x) is 2

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limit as x approaches 0 of (tan(4x))/(2x)

x \to 0 lim (\frac{tan ( 4 x )}{2 x})

2

Solution steps

x \to 0 lim (\frac{tan ( 4 x )}{2 x})

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

= \frac{1}{2} \cdot x \to 0 lim (\frac{tan ( 4 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{1})

= \frac{1}{2} \cdot x \to 0 lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{1})

Plug in the value

x = 0

= \frac{1}{2} \cdot \frac{sec ^{2} ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{1}{2} \cdot \frac{sec ^{2} ( 4 \cdot 0 ) \cdot 4}{1} : 2

= 2

x \to - 7 lim (\frac{4 x - 1}{x + 7})

x \to 8 + lim (\frac{x}{x - 8})

h \to 0 lim (f (x, h) (x + h))

x \to 0 lim ((4 x)^{x})

x \to 0 lim ((1 + x^{2})^{\frac{3}{x}})

What is the limit as x approaches 0 of (tan(4x))/(2x) ?
The limit as x approaches 0 of (tan(4x))/(2x) is 2