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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

: t \to 0 lim (\frac{cos ( t )}{1})

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

Plug in the value

t = 0

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

Simplify

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

= 1

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