Show that the fractional error in ti produced by an error

Question

When the ice point i and the steam point s were chosen as fixed points with 100 degrees between them in the original Celsius scale, the ideal-gas temperature of the ice point was written

θ_i = 100/(r_s-1)

Where rs = lim (P_s/P_i) at constant V.

(a) Show that the fractional error in T_i produced by an error in r, is very nearly 3.73 times the fractional error in rs, or

dT_i/T_i = 3.73 dr_s/r_s.

(b) Any ideal-gas temperature may be written

T = T_ir,

Where r = lim (P/Pi) at constant V. Show that the fractional error in T is

dT/T = (dr/r) + 3.73 dr_s/r_s

(c) Now that the single fixed point of the ideal-gas temperature is a universal constant, show that the fractional error in T is

dT/T = dr/r,

where r = lim(P/P_TP) at constant V.