What is the limit as x approaches 0 of xcot((pix)/2) ?

The limit as x approaches 0 of xcot((pix)/2) is 2/pi

Popular >

limit as x approaches 0 of xcot((pix)/2)

x \to 0 lim (x cot (\frac{π x}{2}))

\frac{2}{π}

Solution steps

x \to 0 lim (x cot (\frac{π x}{2}))

Rewrite for L'Hopital

= x \to 0 lim \frac{x}{\frac{1}{c o t ( \frac{x π}{2} )}}

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{1}{sec ^{2} ( \frac{π 0}{2} ) \frac{π}{2}}

Simplify

\frac{1}{sec ^{2} ( \frac{π 0}{2} ) \frac{π}{2}} : \frac{2}{π}

= \frac{2}{π}

\int (5 + x^{8})^{4} 8 x^{7} d x

\int x^{3} sin (3 x) d x

\frac{d y}{d x} + y = e^{- x}

\frac{5 s}{s ^{2} ( s ^{2} + 16 )}

n = 0 \sum \infty n sin (\frac{1}{n})

What is the limit as x approaches 0 of xcot((pix)/2) ?
The limit as x approaches 0 of xcot((pix)/2) is 2/pi