What is the limit as x approaches 0 of (tan(x))/(6x) ?

The limit as x approaches 0 of (tan(x))/(6x) is 1/6

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limit as x approaches 0 of (tan(x))/(6x)

x \to 0 lim (\frac{tan ( x )}{6 x})

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

x \to 0 lim (\frac{tan ( x )}{6 x})

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

= \frac{1}{6} \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}{6} \cdot x \to 0 lim (\frac{sec ^{2} ( x )}{1})

Plug in the value

x = 0

= \frac{1}{6} \cdot \frac{sec ^{2} ( 0 )}{1}

Simplify

\frac{1}{6} \cdot \frac{sec ^{2} ( 0 )}{1} : \frac{1}{6}

= \frac{1}{6}

- 5 cos (5 t)

x y \frac{d y}{d x} = x^{2} - y^{2}

f (x) = x + 5, at x = 4

(2 x - y) d x + (2 y - x) d y = 0

\frac{d}{d x} ((1 - x)^{- 2})

What is the limit as x approaches 0 of (tan(x))/(6x) ?
The limit as x approaches 0 of (tan(x))/(6x) is 1/6