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

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

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

y \to 0 lim (\frac{sin ( 3 y )}{2 y})

\frac{3}{2}

Decimal

1.5

Solution steps

y \to 0 lim (\frac{sin ( 3 y )}{2 y})

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

= \frac{1}{2} \cdot y \to 0 lim (\frac{sin ( 3 y )}{y})

Apply L'Hopital's Rule

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

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

Plug in the value

y = 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}

x \to \infty - lim (ln (x))

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

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

x \to 3 + lim (\frac{4 x - 1}{6 - 2 x})

x \to 4 lim (\frac{1}{x + 4})

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