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 -1

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

x \to π - lim ((x - π) csc (x))

- 1

Solution steps

x \to π - lim ((x - π) csc (x))

Rewrite for L'Hopital

= x \to π - lim (\frac{x - π}{\frac{1}{c s c ( 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

f (x) = \frac{4 x - 7}{28 x ^{5}}

y = cos^{3} (x)

\int_{0}^{\infty} \frac{1}{x ^{3}} d x

\int (x^{4} + 6 x^{2}) (4 x^{3} + 12 x) d x

\frac{d}{d x} (e^{x} (x - 2))

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 -1