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

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

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limit as x approaches 0 of 1/(sin(5x))

x \to 0 lim (\frac{1}{sin ( 5 x )})

diverges

Solution steps

x \to 0 lim (\frac{1}{sin ( 5 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 ( 5 x )}) = \infty

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

= diverges

a re a y = - x^{2} + 16, x = - 2, y = 0, x = 3

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

x \to (0) + lim (3 x^{(\frac{x}{2})})

\frac{d}{d x} (14 x e^{x})

\int (x + 5) (x - 3) d x

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