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

The limit as θ approaches 0 of (sin(θ))/(4θ) is 1/4

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

θ \to 0 lim (\frac{sin ( θ )}{4 θ})

\frac{1}{4}

Decimal

0.25

Solution steps

θ \to 0 lim (\frac{sin ( θ )}{4 θ})

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

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

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( θ )}{1})

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

Plug in the value

θ = 0

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

Simplify

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

= \frac{1}{4}

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

What is the limit as θ approaches 0 of (sin(θ))/(4θ) ?
The limit as θ approaches 0 of (sin(θ))/(4θ) is 1/4