What is the limit as x approaches 0 of (sin(3x))/(tan(10x)) ?

The limit as x approaches 0 of (sin(3x))/(tan(10x)) is 3/10

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limit as x approaches 0 of (sin(3x))/(tan(10x))

x \to 0 lim (\frac{sin ( 3 x )}{tan ( 10 x )})

\frac{3}{10}

Decimal

0.3

Solution steps

x \to 0 lim (\frac{sin ( 3 x )}{tan ( 10 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{sec ^{2} ( 10 x ) \cdot 10})

Plug in the value

x = 0

= \frac{cos ( 3 \cdot 0 ) \cdot 3}{sec ^{2} ( 10 \cdot 0 ) \cdot 10}

Simplify

\frac{cos ( 3 \cdot 0 ) \cdot 3}{sec ^{2} ( 10 \cdot 0 ) \cdot 10} : \frac{3}{10}

= \frac{3}{10}

What is the limit as x approaches 0 of (sin(3x))/(tan(10x)) ?
The limit as x approaches 0 of (sin(3x))/(tan(10x)) is 3/10