Jika f(x)=x2−2f\left(x\right)=x^2-2f(x)=x2−2 dan g(x)=8x−3g\left(x\right)=8x-3g(x)=8x−3, maka limx→a(f(x)+g(x))=....\lim\limits_{x\to a}\left(f\left(x\right)+g\left(x\right)\right)=....x→alim(f(x)+g(x))=....
limx→a(x2−2)+limx→a(8x−3)\lim\limits_{x\to a}\left(x^2-2\right)+\lim\limits_{x\to a}\left(8x-3\right)x→alim(x2−2)+x→alim(8x−3)
limx→a(8x)+limx→a(x2−1)\lim\limits_{x\to a}\left(8x\right)+\lim\limits_{x\to a}\left(x^2-1\right)x→alim(8x)+x→alim(x2−1)
limx→a(x2−2)+limx→a(3x−8)\lim\limits_{x\to a}\left(x^2-2\right)+\lim\limits_{x\to a}\left(3x-8\right)x→alim(x2−2)+x→alim(3x−8)
limx→a(x−2)+limx→a(3x−8)\lim\limits_{x\to a}\left(x-2\right)+\lim\limits_{x\to a}\left(3x-8\right)x→alim(x−2)+x→alim(3x−8)
limx→a(2−x2)+limx→a(3x+8)\lim\limits_{x\to a}\left(2-x^2\right)+\lim\limits_{x\to a}\left(3x+8\right)x→alim(2−x2)+x→alim(3x+8)
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)=x2−2f\left(x\right)=x^2-2f(x)=x2−2 dan g(x)=8x−3g\left(x\right)=8x-3g(x)=8x−3, maka
limx→a((x2−2)+(8x−3))=limx→a(x2−2)+limx→a(8x−3)\lim\limits_{x\to a}\left(\left(x^2-2\right)+\left(8x-3\right)\right)=\lim\limits_{x\to a}\left(x^2-2\right)+\lim\limits_{x\to a}\left(8x-3\right)x→alim((x2−2)+(8x−3))=x→alim(x2−2)+x→alim(8x−3)