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

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

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

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

7

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= 7

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