What is the limit as x approaches 0 of (1-cos(5x))/(sin(3x)) ?

The limit as x approaches 0 of (1-cos(5x))/(sin(3x)) is 0

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limit as x approaches 0 of (1-cos(5x))/(sin(3x))

x \to 0 lim (\frac{1 - cos ( 5 x )}{sin ( 3 x )})

0

Solution steps

x \to 0 lim (\frac{1 - cos ( 5 x )}{sin ( 3 x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{5 sin ( 5 x )}{cos ( 3 x ) \cdot 3})

Plug in the value

x = 0

= \frac{5 sin ( 5 \cdot 0 )}{cos ( 3 \cdot 0 ) \cdot 3}

Simplify

\frac{5 sin ( 5 \cdot 0 )}{cos ( 3 \cdot 0 ) \cdot 3} : 0

= 0

What is the limit as x approaches 0 of (1-cos(5x))/(sin(3x)) ?
The limit as x approaches 0 of (1-cos(5x))/(sin(3x)) is 0