Prove that if \[ \lim_{x\to a}\,\left[f(x)+g(x)\right]=M\mbox{ and }\lim_{x\to a}\,f(x)=L \] then \[ \lim_{x\to a}\,g(x) \] exists and is equal to $M-L$.
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Lesson Parent:
Problem:
Prove that if
\[
\lim_{x\to a}\,\left[f(x)+g(x)\right]=M\mbox{ and }\lim_{x\to a}\,f(x)=L
\]
then
\[
\lim_{x\to a}\,g(x)
\]
exists and is equal to $M-L$.
Answer:
\[\lim_{x\to a}\,g(x)=M-L\]
