What is the limit as θ approaches 0 of (sin(8θ))/θ ?

The limit as θ approaches 0 of (sin(8θ))/θ is 8

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limit as θ approaches 0 of (sin(8θ))/θ

θ \to 0 lim (\frac{sin ( 8 θ )}{θ})

8

Solution steps

θ \to 0 lim (\frac{sin ( 8 θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 8 θ ) \cdot 8}{1})

= θ \to 0 lim (\frac{cos ( 8 θ ) \cdot 8}{1})

Plug in the value

θ = 0

= \frac{cos ( 8 \cdot 0 ) \cdot 8}{1}

Simplify

\frac{cos ( 8 \cdot 0 ) \cdot 8}{1} : 8

= 8

x \to 0 lim (sin (\frac{π}{6}))

x \to 0 lim (e^{- \frac{1}{x ^{4}}})

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

x \to 1 lim (x^{2} + 2 x - 1)

x \to 3 lim (2 x 12 - x)

What is the limit as θ approaches 0 of (sin(8θ))/θ ?
The limit as θ approaches 0 of (sin(8θ))/θ is 8