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

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

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

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

7

Solution steps

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

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( 7 x ) \cdot 7}{1})

Plug in the value

x = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{1}

Simplify

\frac{cos ( 7 \cdot 0 ) \cdot 7}{1} : 7

= 7

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