What is the limit as θ approaches 0 of (2sin(3θ))/θ ?

The limit as θ approaches 0 of (2sin(3θ))/θ is 6

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limit as θ approaches 0 of (2sin(3θ))/θ

θ \to 0 lim (\frac{2 sin ( 3 θ )}{θ})

6

Solution steps

θ \to 0 lim (\frac{2 sin ( 3 θ )}{θ})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 3 θ ) \cdot 3}{1})

= 2 \cdot θ \to 0 lim (\frac{cos ( 3 θ ) \cdot 3}{1})

Plug in the value

θ = 0

= 2 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

2 \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 6

= 6

\frac{d}{d x} (\frac{7}{x ln ( x )})

\frac{\partial}{\partial y} (x^{2} + z^{2})

\frac{\partial}{\partial x} (a)

f (x) = (\frac{( x - 3 )}{( x + 2 )})^{2} x = - 1

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{3}} d x

What is the limit as θ approaches 0 of (2sin(3θ))/θ ?
The limit as θ approaches 0 of (2sin(3θ))/θ is 6