What is the limit as y approaches+0 of y/(sin(5y)) ?

The limit as y approaches+0 of y/(sin(5y)) is 1/5

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limit as y approaches+0 of y/(sin(5y))

y \to + 0 lim (\frac{y}{sin ( 5 y )})

\frac{1}{5}

Decimal

0.2

Solution steps

y \to 0 lim (\frac{y}{sin ( 5 y )})

Apply L'Hopital's Rule

= y \to 0 lim (\frac{1}{cos ( 5 y ) \cdot 5})

Plug in the value

y = 0

= \frac{1}{cos ( 5 \cdot 0 ) \cdot 5}

cos (5 \cdot 0) \cdot 5 = 5

= \frac{1}{5}

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What is the limit as y approaches+0 of y/(sin(5y)) ?
The limit as y approaches+0 of y/(sin(5y)) is 1/5