Prove that lim if \lim_{x\to a^+}\,f(x)=L and \lim_{x\to a^+}\,g(x)=K.

Problem: 

Prove that
\lim_{x\to a^+}\,[f(x)+g(x)]=L+K
if
\lim_{x\to a^+}\,f(x)=L
and
\lim_{x\to a^+}\,g(x)=K.

Answer: 

It is true that \lim_{x\to a^+}\,[f(x)+g(x)]=L+K if \lim_{x\to a^+}\,f(x)=L and \lim_{x\to a^+}\,g(x)=K.