What is the limit as θ approaches 0 of (sin(3θ))/(2θ) ?

The limit as θ approaches 0 of (sin(3θ))/(2θ) is 3/2

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limit as θ approaches 0 of (sin(3θ))/(2θ)

θ \to 0 lim (\frac{sin ( 3 θ )}{2 θ})

\frac{3}{2}

Solution steps

θ \to 0 lim (\frac{sin ( 3 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 ( 3 θ )}{θ})

Apply L'Hopital's Rule

: θ \to 0 lim (\frac{cos ( 3 θ ) \cdot 3}{1})

= \frac{1}{2} \cdot θ \to 0 lim (\frac{cos ( 3 θ ) \cdot 3}{1})

Plug in the value

θ = 0

= \frac{1}{2} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

\frac{1}{2} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : \frac{3}{2}

= \frac{3}{2}

\int cot^{3} (x) csc^{4} (x) d x

f (x) = 4 x - 3

y = 4 e^{- x} + e^{3 x}

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x - 1)

\frac{d}{d x} (\frac{x - y}{x + y})

What is the limit as θ approaches 0 of (sin(3θ))/(2θ) ?
The limit as θ approaches 0 of (sin(3θ))/(2θ) is 3/2