d$)$ The stability of a unity feedback control system is to be investigated using Bode analysis.

The forward transfer function of the system is:

$G(s)=\frac{K}{(s+2)(s+3)(s+5)}$

Assuming $K=40,$ sketch on a linear$-$log graph paper, the Bode magnitude and phase angle curves using piecewise linear asymptotic approximations and hence;

i$)$ Obtain the range of values of $K$ for which the system is stable.