What is the limit as θ approaches 0 of sin(θ)cot(2θ) ?

The limit as θ approaches 0 of sin(θ)cot(2θ) is 1/2

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limit as θ approaches 0 of sin(θ)cot(2θ)

θ \to 0 lim (sin (θ) cot (2 θ))

\frac{1}{2}

Decimal

0.5

Solution steps

θ \to 0 lim (sin (θ) cot (2 θ))

Rewrite for L'Hopital

= θ \to 0 lim (\frac{sin ( θ )}{\frac{1}{c o t ( 2 θ )}})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( θ )}{sec ^{2} ( 2 θ ) \cdot 2})

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

Plug in the value

θ = 0

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

Simplify

\frac{cos ( 0 )}{sec ^{2} ( 2 \cdot 0 ) \cdot 2} : \frac{1}{2}

= \frac{1}{2}

x \to 0 + lim (tan (9 x))

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

x \to 1 lim (\frac{9 x ^{8}}{5 x ^{4}})

x \to \infty lim (\frac{sin ( x )}{x ^{4}})

x \to \infty lim ((\frac{( x + 1 )}{x - 1})^{x - 1})

What is the limit as θ approaches 0 of sin(θ)cot(2θ) ?
The limit as θ approaches 0 of sin(θ)cot(2θ) is 1/2