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 [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

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

x \to 0 - lim (sec (x)) = 1

= \frac{1}{2} \cdot \frac{\frac{1}{π}}{1}

Simplify

\frac{1}{2} \cdot \frac{\frac{1}{π}}{1} : \frac{1}{2 π}

= \frac{1}{2 π}

n = 0 \sum \infty 2 n - 1

\frac{\partial}{\partial x} (\frac{y}{x ( x + y )})

x \to 7 lim (\frac{x + 8}{x - 7})

\int - \frac{1}{\frac{2}{x} y} d y

sin (tan (5 x))

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)