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 Notation

0.31830 \dots

Solution steps

x \to 0 lim (x cot (π x))

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (x cot (π x)) = \frac{1}{π}

x \to 0 + lim (x cot (π x)) = \frac{1}{π}

= \frac{1}{π}

x \to 4 lim (3 x^{2} - 2 x + 6)

x \to 0 + lim (x cot (x))

x \to 0 lim (∣ x ∣)

y \to \infty lim (\frac{3 + \frac{2}{y ^{3}} - 3 y ^{4}}{9 y ^{4} - \frac{5}{y ^{2}} - 3})

x \to \infty lim (\frac{3 x + 1}{4 x ^{2} - 3 x - 7})

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