# 4.2 Linear Approximation # Art Belmonte, Summer 1996 # These are the shaded gray examples which appear in Section 4.2. # In-line plots have been removed to conserve disk space. > restart; with(plots): > a:=3/2; b:=3/2; m:=-1; > y:=m*(x - a) + b; a := 3/2 b := 3/2 m := -1 y := -x + 3 > L:=unapply(y, x); L := x -> -x + 3 > unassign('y'); > p1:=plot(L(x), x=1..2): > eq:=3*x*y = x^3 + y^3; > p2:=implicitplot(eq, x=1..2, y=1..2, scaling=constrained): > display([p1, p2]); 3 3 eq := 3 x y = x + y > subs(x=1.51, eq); fsolve(", y=1.4..1.6); 3 4.53 y = 3.442951 + y 1.489436032 > L(1.51); 1.49 >