# 4.3 Related Rates # Art Belmonte, Summer 1996 # These are the shaded gray examples which appear in Section 4.3. # In-line plots have been removed to conserve disk space. > restart; > 1/30 = 1/u(t) + 1/v(t); 1 1 1/30 = ---- + ---- u(t) v(t) > diff(", t); d d -- u(t) -- v(t) dt dt 0 = - ------- - ------- 2 2 u(t) v(t) > vrate:=solve(", diff(v(t), t)); /d \ 2 |-- u(t)| v(t) \dt / vrate := - --------------- 2 u(t) > 1/30 = 1/90 + 1/V; imagelength:=solve(", V); 1/30 = 1/90 + 1/V imagelength := 45 > imagerate:=subs(diff(u(t), t)=3, > v(t)=imagelength, u(t)=90, vrate); imagerate := -3/4 >