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

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

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

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

diverges

Solution steps

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

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

= diverges

x \to 0 + lim (\frac{ln ( x )}{x - 1})

x \to - 1 lim (\frac{x ^{2} - 2}{x ^{2} - 5 x - 6})

x \to \infty lim (\frac{x ^{2} - 9}{x \cdot ( x ^{2} + 1 )})

x \to \infty lim (\frac{x ^{2} - 5 x + 6}{x - 2})

x \to \infty lim (ln ((1 - \frac{3}{x})^{x}))

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