What is the limit as x approaches 0 of (sin(7x))/(tan(11x)) ?

The limit as x approaches 0 of (sin(7x))/(tan(11x)) is 7/11

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limit as x approaches 0 of (sin(7x))/(tan(11x))

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

\frac{7}{11}

Solution steps

x \to 0 lim (\frac{sin ( 7 x )}{tan ( 11 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{sec ^{2} ( 11 x ) \cdot 11})

= x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{sec ^{2} ( 11 x ) \cdot 11})

Plug in the value

x = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 11 \cdot 0 ) \cdot 11}

Simplify

\frac{cos ( 7 \cdot 0 ) \cdot 7}{sec ^{2} ( 11 \cdot 0 ) \cdot 11} : \frac{7}{11}

= \frac{7}{11}

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What is the limit as x approaches 0 of (sin(7x))/(tan(11x)) ?
The limit as x approaches 0 of (sin(7x))/(tan(11x)) is 7/11