What is the limit as x approaches 0 of (tan(x))/(5x) ?

The limit as x approaches 0 of (tan(x))/(5x) is 1/5

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limit as x approaches 0 of (tan(x))/(5x)

x \to 0 lim (\frac{tan ( x )}{5 x})

\frac{1}{5}

Decimal Notation

0.2

Solution steps

x \to 0 lim (\frac{tan ( x )}{5 x})

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

= \frac{1}{5} \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}{5} \cdot x \to 0 lim (\frac{sec ^{2} ( x )}{1})

Plug in the value

x = 0

= \frac{1}{5} \cdot \frac{sec ^{2} ( 0 )}{1}

Simplify

\frac{1}{5} \cdot \frac{sec ^{2} ( 0 )}{1} : \frac{1}{5}

= \frac{1}{5}

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 0

(e^{x} cos (y) + 2 x) d x - (e^{x} sin (y)) d y = 0

x^{^{'}} = (x - 4)^{2}

\frac{( e ^{2 p} + 1 )}{3 e ^{2 p}}

x \to 7 + lim (- 2 x^{2} + 2)

What is the limit as x approaches 0 of (tan(x))/(5x) ?
The limit as x approaches 0 of (tan(x))/(5x) is 1/5