Question

Please help me with this question.

Answer 1

Part (a)

We need to consider

`x=(1)/(k\pi), k \in \mathbb{Z}`

`f\left((1)/(k\pi) \right)=\tan (k\pi)</p><p>`

tan(x) has a period of pi, so this is equal to tan(0)=0.

Part (b)

We need to consider

`x=(4)/((4n+1)\pi), n \in \mathbb{Z} \\ \\ f \left((4)/((4n+1)\pi) \right)=\tan \left(((4n+1)\pi)/(4) \right) \\ \\ =\tan \left(\pi n+(\pi)/(4) \right) \\ \\ =1`

Part (c)

We see that 1/x approaches infinity, and hence the limit does not exist.