What is the limit as x approaches 0 of (sin(9x))/(sin(3x)) ?

The limit as x approaches 0 of (sin(9x))/(sin(3x)) is 3

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limit as x approaches 0 of (sin(9x))/(sin(3x))

x \to 0 lim (\frac{sin ( 9 x )}{sin ( 3 x )})

3

Solution steps

x \to 0 lim (\frac{sin ( 9 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 ( 9 x )}{sin ( 3 x )}) = 3

x \to 0 + lim (\frac{sin ( 9 x )}{sin ( 3 x )}) = 3

= 3

\int - 4 e^{x} sin (4 y) d y

\int - x^{\frac{1}{2}} d x

\int \frac{x}{x ^{4} + x ^{2} + 1} d x

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{4}}{x ^{2} + 1})

x \to \infty lim (x^{2} - 9)

What is the limit as x approaches 0 of (sin(9x))/(sin(3x)) ?
The limit as x approaches 0 of (sin(9x))/(sin(3x)) is 3