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

y = lo g_{e} (x)

\int - \frac{7}{x ^{8}} d x

f (x) = x^{2} + 9 x, at x = - 8

\int x (ln (x) + e^{x}) d x

f (x) = 1 - x^{2}, at x = 2

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