What is the limit as x approaches 2-of csc((pix)/2) ?

The limit as x approaches 2-of csc((pix)/2) is infinity

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limit as x approaches 2-of csc((pix)/2)

x \to 2 - lim (csc (\frac{π x}{2}))

\infty

Solution steps

x \to 2 - lim (csc (\frac{π x}{2}))

Express with sin, cos

= x \to 2 - lim (\frac{1}{sin ( \frac{π x}{2} )})

For

x

approaching

2

from the left

, x < 2 \Rightarrow sin (\frac{π x}{2}) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

What is the limit as x approaches 2-of csc((pix)/2) ?
The limit as x approaches 2-of csc((pix)/2) is infinity