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

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

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

θ \to 0 lim (\frac{( sin ( 2 θ ) )}{θ})

2

Solution steps

θ \to 0 lim (\frac{sin ( 2 θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 2 θ ) \cdot 2}{1})

= θ \to 0 lim (\frac{cos ( 2 θ ) \cdot 2}{1})

Plug in the value

θ = 0

= \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

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

= 2

x \to 0 + lim ((3 x)^{x^{2}})

x \to 2 lim (- x^{2} + 2 x)

x \to 3 lim (- 6 x^{6})

x \to \infty lim (0 - x)

x \to \infty lim (0.1)

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