What is the limit as x approaches 0 of 2/(-sin(x)) ?

The limit as x approaches 0 of 2/(-sin(x)) is diverges

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limit as x approaches 0 of 2/(-sin(x))

x \to 0 lim (\frac{2}{- sin ( x )})

diverges

Solution steps

x \to 0 lim (\frac{2}{- 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{2}{- sin ( x )}) = - \infty

x \to 0 - lim (\frac{2}{- sin ( x )}) = \infty

= diverges

x \to - \frac{5}{2} lim (\frac{( 8 x ^{3} + 125 )}{6 x ^{2} + 23 x + 20})

x \to \infty lim (14 x)

x \to 1 lim (\frac{x + 1}{x})

x \to \infty lim (5 - (- 2))

h \to 0 lim (\frac{x ^{2} + 2 x h + h ^{2} + 1}{h} - \frac{x ^{2} + 1}{h})

What is the limit as x approaches 0 of 2/(-sin(x)) ?
The limit as x approaches 0 of 2/(-sin(x)) is diverges