What is the limit as θ approaches 0 of (sin(θ))/(2θ) ?

The limit as θ approaches 0 of (sin(θ))/(2θ) is 1/2

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limit as θ approaches 0 of (sin(θ))/(2θ)

θ \to 0 lim (\frac{sin ( θ )}{2 θ})

\frac{1}{2}

Decimal

0.5

Solution steps

θ \to 0 lim (\frac{sin ( θ )}{2 θ})

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

= \frac{1}{2} \cdot θ \to 0 lim (\frac{sin ( θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( θ )}{1})

= \frac{1}{2} \cdot θ \to 0 lim (\frac{cos ( θ )}{1})

Plug in the value

θ = 0

= \frac{1}{2} \cdot \frac{cos ( 0 )}{1}

Simplify

\frac{1}{2} \cdot \frac{cos ( 0 )}{1} : \frac{1}{2}

= \frac{1}{2}

x \to 3 lim (\frac{x + 33 - 6}{x - 3})

x \to 2 + lim (\frac{1}{x - 3})

x \to 4 lim (3 x - 5)

x \to \infty lim (- 5, x)

x \to 0 lim (x^{2} \cdot ln (- x))

What is the limit as θ approaches 0 of (sin(θ))/(2θ) ?
The limit as θ approaches 0 of (sin(θ))/(2θ) is 1/2