What is the limit as x approaches 0 of (sin(5x))/(tan(6x)) ?

The limit as x approaches 0 of (sin(5x))/(tan(6x)) is 5/6

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limit as x approaches 0 of (sin(5x))/(tan(6x))

x \to 0 lim (\frac{sin ( 5 x )}{tan ( 6 x )})

\frac{5}{6}

Decimal Notation

0.83333 \dots

Solution steps

x \to 0 lim (\frac{sin ( 5 x )}{tan ( 6 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{sec ^{2} ( 6 x ) \cdot 6})

= x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{sec ^{2} ( 6 x ) \cdot 6})

Plug in the value

x = 0

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{sec ^{2} ( 6 \cdot 0 ) \cdot 6}

Simplify

\frac{cos ( 5 \cdot 0 ) \cdot 5}{sec ^{2} ( 6 \cdot 0 ) \cdot 6} : \frac{5}{6}

= \frac{5}{6}

\int \frac{1}{x ( 4 - ln ^{2} ( x ) )} d x

f (x) = \frac{- 9 x}{2 x - 1}

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\frac{d}{d x} (se xx)

\int_{- 1}^{- 0.5} 1.5 x^{2} d x

What is the limit as x approaches 0 of (sin(5x))/(tan(6x)) ?
The limit as x approaches 0 of (sin(5x))/(tan(6x)) is 5/6