f1 := (x,y) -> 8*x^2*y^2/(x^4+y^4); x1:=0; y1:=0; f2 := (x,y) -> sin(x+y)/(x+y); x2:=0; y2:=0; f3 := (x,y) -> (x^2+y^2-2*x-2*y)/(x^2+y^2-2*x+2*y+2);x3:=1;y3:=-1; f4 := (x,y,z) -> x*exp(z) + ln(2*x-y); x4:=2;y4:=3;z4:=0; f5 := (x,y) -> (x^3+x*y^2)/(x^2+y^2);x5:=0;y5:=0; Limit(f1(x, y1 + m*(x-x1)),x=x1) = limit(f1(x, y1 + m*(x-x1)),x=x1); Limit(f2(x, y2 + m*(x-x2)),x=x2) = limit(f2(x, y2 + m*(x-x2)),x=x2); F := (x,y) -> x+y; G := t -> sin(t)/t; (G@F)(x,y); Limit(f3(x, y3 + m*(x-x3)),x=x3) = limit(f3(x, y3 + m*(x-x3)),x=x3); Num := numer(f3(x,y)); Idom := 1/denom(f3(x,y)); (x-1)^2+(y+1)^2 = expand((x-1)^2+(y+1)^2); L := evalm([x4,y4,z4] + t*[m1,m2,m3]); Limit(f4(L[1],L[2],L[3]),t=0) = limit(f4(L[1],L[2],L[3]),t=0); f4(x4,y4,z4); Limit(f5(x,m*x),x=x5) = limit(f5(x,m*x),x=x5); Limit(f5(x,x^2),x=x5) = limit(f5(x,x^2),x=x5); Limit(f5(y^2,y),y=y5) = limit(f5(y^2,y),y=y5); f5(x,y); simplify(");