What is the limit as x approaches 0 of (sin(5x))/(sin(9x)) ?

The limit as x approaches 0 of (sin(5x))/(sin(9x)) is 5/9

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limit as x approaches 0 of (sin(5x))/(sin(9x))

x \to 0 lim (\frac{sin ( 5 x )}{sin ( 9 x )})

\frac{5}{9}

Decimal Notation

0.55555 \dots

Solution steps

x \to 0 lim (\frac{sin ( 5 x )}{sin ( 9 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 ( 9 x )}) = \frac{5}{9}

x \to 0 + lim (\frac{sin ( 5 x )}{sin ( 9 x )}) = \frac{5}{9}

= \frac{5}{9}

\int x (3 x^{2} - 5) d x

3 x^{2} - 2 y^{3} \frac{d y}{d x} = 0

\frac{\partial}{\partial y} (x^{2} - y^{2})

\int x^{2} + 4 x + 3 d x

\int \frac{sec ( x )}{1 - tan ( x )} d x

What is the limit as x approaches 0 of (sin(5x))/(sin(9x)) ?
The limit as x approaches 0 of (sin(5x))/(sin(9x)) is 5/9