What is the limit as t approaches 0 of (sin(2t))/t ?

The limit as t approaches 0 of (sin(2t))/t is 2

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limit as t approaches 0 of (sin(2t))/t

t \to 0 lim (\frac{sin ( 2 t )}{t})

2

Solution steps

t \to 0 lim (\frac{sin ( 2 t )}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{cos ( 2 t ) \cdot 2}{1})

= t \to 0 lim (\frac{cos ( 2 t ) \cdot 2}{1})

Plug in the value

t = 0

= \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : 2

= 2

x \to 0 + lim (sin (x) \cdot ln (x))

4 y^{^{''}} - 9 y = 0

y = \frac{1}{t + 1}

\frac{d}{d x} (\frac{1}{4} x^{3} - 2 x)

\frac{d}{d x} (sin (e^{- x}))

What is the limit as t approaches 0 of (sin(2t))/t ?
The limit as t approaches 0 of (sin(2t))/t is 2