What is the limit as t approaches 0 of (sin(-4t))/t ?

The limit as t approaches 0 of (sin(-4t))/t is -4

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limit as t approaches 0 of (sin(-4t))/t

t \to 0 lim (\frac{sin ( - 4 t )}{t})

- 4

Solution steps

t \to 0 lim (\frac{sin ( - 4 t )}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{- cos ( 4 t ) \cdot 4}{1})

= t \to 0 lim (\frac{- cos ( 4 t ) \cdot 4}{1})

Plug in the value

t = 0

= \frac{- cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{- cos ( 4 \cdot 0 ) \cdot 4}{1} : - 4

= - 4

h

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

x \to a lim (c f (x))

f (x) = 1 - 2 x

\frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{36 x})

What is the limit as t approaches 0 of (sin(-4t))/t ?
The limit as t approaches 0 of (sin(-4t))/t is -4