What is the limit as x approaches 0 of (3-3cos(x))/(sin^2(x)) ?

The limit as x approaches 0 of (3-3cos(x))/(sin^2(x)) is 3/2

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limit as x approaches 0 of (3-3cos(x))/(sin^2(x))

x \to 0 lim (\frac{3 - 3 cos ( x )}{sin ^{2} ( x )})

\frac{3}{2}

Decimal

1.5

Solution steps

x \to 0 lim (\frac{3 - 3 cos ( x )}{sin ^{2} ( x )})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{3 sin ( x )}{sin ( 2 x )})

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

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

= \frac{3}{2}

What is the limit as x approaches 0 of (3-3cos(x))/(sin^2(x)) ?
The limit as x approaches 0 of (3-3cos(x))/(sin^2(x)) is 3/2