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

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

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

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

\frac{3}{2}

Decimal Notation

1.5

Solution steps

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

Apply L'Hopital's Rule

: w \to 0 lim (\frac{- sin ( w ) + 2 sin ( 2 w )}{sin ( 2 w )})

= w \to 0 lim (\frac{- sin ( w ) + 2 sin ( 2 w )}{sin ( 2 w )})

Apply L'Hopital's Rule

: w \to 0 lim (\frac{- cos ( w ) + 4 cos ( 2 w )}{cos ( 2 w ) \cdot 2})

= w \to 0 lim (\frac{- cos ( w ) + 4 cos ( 2 w )}{cos ( 2 w ) \cdot 2})

Plug in the value

w = 0

= \frac{- cos ( 0 ) + 4 cos ( 2 \cdot 0 )}{cos ( 2 \cdot 0 ) \cdot 2}

Simplify

\frac{- cos ( 0 ) + 4 cos ( 2 \cdot 0 )}{cos ( 2 \cdot 0 ) \cdot 2} : \frac{3}{2}

= \frac{3}{2}

x \to 0 + lim (x^{2} (ln (x^{2})))

x \to 3 lim (tan (\frac{π x}{4}))

x \to 0 lim (x \frac{1}{x})

x \to 0 lim (tan (x) (ln (x)))

x \to 0 lim (x^{2} (ln (x))^{2})

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