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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= \frac{1}{2}

\int \frac{( x ^{2} + 1 )}{x ^{3} + 1} d x

n = 1 \sum \infty \frac{1}{( 4 n ^{2} - 1 )}

\int_{0}^{\frac{π}{2}} cos (t) d t

y^{^{'''}} + 3 y^{^{''}} - 4 y^{^{'}} - 12 = 0

\frac{d ^{2} x}{d t ^{2}} + 4 x = sin (1 t), x (0) = 1

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