What is the limit as x approaches 0-of xcot(pix) ?

The limit as x approaches 0-of xcot(pix) is 1/pi

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limit as x approaches 0-of xcot(pix)

x \to 0 - lim (x cot (π x))

\frac{1}{π}

Decimal

0.31830 \dots

Solution steps

x \to 0 - lim (x cot (π x))

Rewrite for L'Hopital

= x \to 0 - lim (\frac{x}{\frac{1}{c o t ( x π )}})

Apply L'Hopital's Rule

= x \to 0 - lim (\frac{1}{sec ^{2} ( π x ) π})

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( π 0 ) π}

sec^{2} (π 0) π = π

= \frac{1}{π}

What is the limit as x approaches 0-of xcot(pix) ?
The limit as x approaches 0-of xcot(pix) is 1/pi