Question

which two points are midpoint between the x - intercept and each of the vertical asymptotes of the function y= 5 cot(1/4x)

Answer 1

`\begin{gathered} y=\cot ((1)/(4)x)=0 \\ x=2(n-1)\pi \\ n\in N \end{gathered}`

The asymptotes are:

`(x)/(4\pi)\\otin Z`

So, the midpoints are:

`\begin{gathered} (0+2\pi)/(2)=\pi \\ (0-2\pi)/(2)=-\pi \end{gathered}`
`\begin{gathered} (\pi,5) \\ (-\pi,-5) \end{gathered}`