i := vector([1,0,0]): j:=vector([0,1,0]): k:=vector([0,0,1]): r := t -> cos(t)*i + sin(t)*j + t*k; r(0); r(Pi/2); r(Pi); with(plots): spacecurve(evalm(r(t)), t=0..4*Pi, color=YELOW,axes=NORMAL); f := t -> expand(r(t)/t): `f(t)` = f(t); Limit(`f(t)`,t=t0) = expand(limit(f(t),t=t0)); Limit(`f(t)`,t=0) = limit(f(t),t=0); Limit(`f(t)`,t=Pi/4) = expand(limit(f(t),t=Pi/4)); evalf(",3); Limit(`f(t)`,t=3*Pi/4) = expand(simplify(limit(f(t),t=3*Pi/4))); Limit(a*`f(t)` + b*`r(t)`,t=s) = limit(a*f(t)+b*r(t),t=s);