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

\int e^{- 9 x} d x

5 ln (x), x ln (x)

\int \frac{1}{3 x ^{2} - 2 x + 5} d x

\frac{d}{d x} (x^{4} - 8 x^{2} + 3)

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