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

The limit as x approaches 0 of x/(sin(2x)) is 1/2

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

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

cos (2 \cdot 0) \cdot 2 = 2

= \frac{1}{2}

a re a (2) sin (x), [0, π]

\int \frac{( x ^{2} - x + 12 )}{( x ^{3} + 3 x )} d x

\int 2 - y d y

t a y l or \frac{1}{x ^{2}}, 7

d er i v a t i v e x^{\frac{5}{2}} e^{x}

What is the limit as x approaches 0 of x/(sin(2x)) ?
The limit as x approaches 0 of x/(sin(2x)) is 1/2