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

The limit as x approaches 0-of 1/(sin(x)) is -infinity

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

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

- \infty

Solution steps

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

For

x

approaching

0

from the left

, x < 0 \Rightarrow sin (x) < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

- 5 + 9 x

\frac{d y}{d t} = 2 t y^{2}

\int (x - 2 π) d x

\int (sin^{4} (x) + cos^{4} (x)) d x

\frac{d y}{d x} = \frac{2 y}{x} + y

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