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

y = 3 x + 6 cos (x), (\frac{π}{3}, π + 3)

\frac{x ^{2} - 1}{x ^{2} + x + 1}

\int e^{x} + 1 d x

\int x (x^{5} + 3) d x

y = (x^{2} + 8)^{2} - 4 x

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