What is the limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x)) ?

The limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x)) is 1/(2pi)

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limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x))

x \to 0 lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})

\frac{1}{2 π}

Decimal Notation

0.15915 \dots

Solution steps

x \to 0 lim (\frac{cot ( π x ) sin ( x )}{2 sec ( 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 (\frac{cot ( π x ) sin ( x )}{2 sec ( x )}) = \frac{1}{2 π}

x \to 0 + lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )}) = \frac{1}{2 π}

= \frac{1}{2 π}

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What is the limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x)) ?
The limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x)) is 1/(2pi)