Jika f(x)=4x dan g(x)=3x+1, maka x→alim(f(x)−g(x))=....
x→alim4x−x→alim(3x+1)
x→alim(3x+1)−x→alim4x
x→alim3x+x→alim(4x+1)
x→alim4x−x→alim(3x−1)
x→alim3x−x→alim(4x−1)
Jika f(x)f\left(x\right)f(x) dan g(x)g\left(x\right)g(x) adalah fungsi-fungsi dari xxx dan ccc adalah suatu konstanta, maka
limx→c(f(x)−g(x))=limx→cf(x)−limx→cg(x)\lim\limits_{x\to c}\left(f\left(x\right)-g\left(x\right)\right)=\lim\limits_{x\to c}f\left(x\right)-\lim\limits_{x\to c}g\left(x\right)x→clim(f(x)−g(x))=x→climf(x)−x→climg(x)
Dengan demikian,
Jika f(x)=4xf\left(x\right)=4xf(x)=4x dan g(x)=3x+1g\left(x\right)=3x+1g(x)=3x+1 maka
limx→a(f(x)−g(x))=limx→a4x−limx→a(3x+1)\lim\limits_{x\to a}\left(f\left(x\right)-g\left(x\right)\right)=\lim\limits_{x\to a}4x-\lim\limits_{x\to a}\left(3x+1\right)x→alim(f(x)−g(x))=x→alim4x−x→alim(3x+1)