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

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

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

x \to π - lim (\frac{1}{sin ( x )})

\infty

Solution steps

x \to π - lim (\frac{1}{sin ( x )})

For

x

approaching

π

from the left

, x < π \Rightarrow sin (x) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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