What is the limit as x approaches 0 of (sin(10x))/(sin(3x)) ?

The limit as x approaches 0 of (sin(10x))/(sin(3x)) is 10/3

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limit as x approaches 0 of (sin(10x))/(sin(3x))

x \to 0 lim (\frac{sin ( 10 x )}{sin ( 3 x )})

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

x \to 0 lim (\frac{sin ( 10 x )}{sin ( 3 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 ( 10 x )}{sin ( 3 x )}) = \frac{10}{3}

x \to 0 + lim (\frac{sin ( 10 x )}{sin ( 3 x )}) = \frac{10}{3}

= \frac{10}{3}

What is the limit as x approaches 0 of (sin(10x))/(sin(3x)) ?
The limit as x approaches 0 of (sin(10x))/(sin(3x)) is 10/3