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

The limit as x approaches 0 of (tan(x))/(4x) is 1/4

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

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

\frac{1}{4}

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{4}

\int \frac{2 x}{x} d x

x \to 0 lim (+ (e^{x}))

\int (3 x + 1)^{2} d x

e^{- 0.5 x}

\frac{d}{d t} ((A t^{2} + Bt + C) (sin (2 t) + cos (2 t)))

What is the limit as x approaches 0 of (tan(x))/(4x) ?
The limit as x approaches 0 of (tan(x))/(4x) is 1/4