What is the limit as θ approaches 0 of (sin(9θ))/θ ?

The limit as θ approaches 0 of (sin(9θ))/θ is 9

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limit as θ approaches 0 of (sin(9θ))/θ

θ \to 0 lim (\frac{sin ( 9 θ )}{θ})

9

Solution steps

θ \to 0 lim (\frac{sin ( 9 θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 9 θ ) \cdot 9}{1})

= θ \to 0 lim (\frac{cos ( 9 θ ) \cdot 9}{1})

Plug in the value

θ = 0

= \frac{cos ( 9 \cdot 0 ) \cdot 9}{1}

Simplify

\frac{cos ( 9 \cdot 0 ) \cdot 9}{1} : 9

= 9

- \frac{1}{x}

x \to - \infty lim (\frac{( 3 ^{6 x} + 6 )}{( 3 ^{2 x} + 4 )})

\frac{d}{d x} (lo g_{e} (x^{2}))

t \to \infty lim (t)

(\frac{2 + 5 z}{5 z}) (15 - 2 z)

What is the limit as θ approaches 0 of (sin(9θ))/θ ?
The limit as θ approaches 0 of (sin(9θ))/θ is 9