What is the limit as x approaches 0 of (sin(5x))/(sin(10x)) ?

The limit as x approaches 0 of (sin(5x))/(sin(10x)) is 1/2

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limit as x approaches 0 of (sin(5x))/(sin(10x))

x \to 0 lim (\frac{sin ( 5 x )}{sin ( 10 x )})

\frac{1}{2}

Solution steps

x \to 0 lim (\frac{sin ( 5 x )}{sin ( 10 x )})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (\frac{sin ( 5 x )}{sin ( 10 x )}) = \frac{1}{2}

x \to 0 + lim (\frac{sin ( 5 x )}{sin ( 10 x )}) = \frac{1}{2}

= \frac{1}{2}

\int - 0.92 t + 1.86 d t

\int x \cdot tan (x^{2}) d x

3 \cdot e^{- s}

x (x^{2} - 4 x + 5)^{4}, at x = 2

x \to 4 + lim (\frac{x + 2}{x - 4})

What is the limit as x approaches 0 of (sin(5x))/(sin(10x)) ?
The limit as x approaches 0 of (sin(5x))/(sin(10x)) is 1/2