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

The limit as x approaches pi-of (pi-x)csc(x) is 1

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

x \to π - lim ((π - x) csc (x))

1

Solution steps

x \to π - lim ((π - x) csc (x))

Express with sin, cos

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

Apply L'Hopital's Rule

: x \to π - lim (\frac{- 1}{cos ( x )})

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

Plug in the value

x = π

= \frac{- 1}{cos ( π )}

Simplify

\frac{- 1}{cos ( π )} : 1

= 1

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What is the limit as x approaches pi-of (pi-x)csc(x) ?
The limit as x approaches pi-of (pi-x)csc(x) is 1