What is the limit as θ approaches 0 of (sin(4θ))/θ ?

The limit as θ approaches 0 of (sin(4θ))/θ is 4

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limit as θ approaches 0 of (sin(4θ))/θ

θ \to 0 lim (\frac{sin ( 4 θ )}{θ})

4

Solution steps

θ \to 0 lim (\frac{sin ( 4 θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 4 θ ) \cdot 4}{1})

= θ \to 0 lim (\frac{cos ( 4 θ ) \cdot 4}{1})

Plug in the value

θ = 0

= \frac{cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{cos ( 4 \cdot 0 ) \cdot 4}{1} : 4

= 4

f (x) = 8 x^{2} + 4 e^{- 0.5 x}

3 x

(x - y) d x + d y = 0

x \to 0 lim (\frac{g ( x )}{f ( x )})

\int_{0}^{3} 4 d x

What is the limit as θ approaches 0 of (sin(4θ))/θ ?
The limit as θ approaches 0 of (sin(4θ))/θ is 4