What is the limit as x approaches pi-of (x+pi)csc(x) ?

The limit as x approaches pi-of (x+pi)csc(x) is infinity

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limit as x approaches pi-of (x+pi)csc(x)

x \to π - lim ((x + π) csc (x))

\infty

Solution steps

x \to π - lim ((x + π) csc (x))

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to π - lim (x + π) \cdot x \to π - lim (csc (x))

x \to π - lim (x + π) = 2 π

x \to π - lim (csc (x)) = \infty

= 2 π \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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f (x) = \frac{x}{1 + x ^{2}}, (3, 0.3)

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What is the limit as x approaches pi-of (x+pi)csc(x) ?
The limit as x approaches pi-of (x+pi)csc(x) is infinity