What is the limit as x approaches 0 of 4/(sin(5x)) ?

The limit as x approaches 0 of 4/(sin(5x)) is diverges

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limit as x approaches 0 of 4/(sin(5x))

x \to 0 lim (\frac{4}{sin ( 5 x )})

diverges

Solution steps

x \to 0 lim (\frac{4}{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{4}{sin ( 5 x )}) = \infty

x \to 0 - lim (\frac{4}{sin ( 5 x )}) = - \infty

= diverges

What is the limit as x approaches 0 of 4/(sin(5x)) ?
The limit as x approaches 0 of 4/(sin(5x)) is diverges