What is the limit as t approaches 0 of (sin(-3t))/t ?

The limit as t approaches 0 of (sin(-3t))/t is -3

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limit as t approaches 0 of (sin(-3t))/t

t \to 0 lim (\frac{sin ( - 3 t )}{t})

- 3

Solution steps

t \to 0 lim (\frac{sin ( - 3 t )}{t})

Apply L'Hopital's Rule

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

= t \to 0 lim (\frac{- cos ( 3 t ) \cdot 3}{1})

Plug in the value

t = 0

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

Simplify

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

= - 3

x \to 0 - lim (x^{2} \cdot ln (- x))

x \to 0 lim ((\frac{1}{x}) (\frac{1}{3} - \frac{1}{x + 9}))

x \to 1 lim (\frac{x - 1}{2})

x \to - \frac{π}{2} - lim (sec (x))

x \to 2 - lim (x - 3)

What is the limit as t approaches 0 of (sin(-3t))/t ?
The limit as t approaches 0 of (sin(-3t))/t is -3