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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

y = 0

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

Simplify

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

= 1

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