What is the limit as x approaches 0 of 1/(sin(3x)) ?

The limit as x approaches 0 of 1/(sin(3x)) is diverges

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limit as x approaches 0 of 1/(sin(3x))

x \to 0 lim (\frac{1}{sin ( 3 x )})

diverges

Solution steps

x \to 0 lim (\frac{1}{sin ( 3 x )})

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

then the limit does not exist

x \to 0 + lim (\frac{1}{sin ( 3 x )}) = \infty

x \to 0 - lim (\frac{1}{sin ( 3 x )}) = - \infty

= diverges

f (x) = 2 x^{2}, at 3

\int_{- 2}^{3} \frac{12}{x ^{4}} d x

f (x) = sin (sin (x)), at x = 3 π

\int x^{9} e^{7 x^{5}} d x

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

What is the limit as x approaches 0 of 1/(sin(3x)) ?
The limit as x approaches 0 of 1/(sin(3x)) is diverges