Calculus Level 4

Read the statements carefully.

\([1]\). If \(f(x)<g(x)\) for all \(x\), then \(\displaystyle \lim_{x\to c} f(x) < \displaystyle \lim_{x\to c} g(x)\) provided that these limits exist.

\([2]\). If both \(\displaystyle \lim_{x\to c} f(x)\) and \(\displaystyle \lim_{x\to c} g(x)\) do not exist, then it is impossible for \(\displaystyle \lim_{x\to c} (f(x)+g(x))\) to exist.

\([3]\). If \(\displaystyle \lim_{x\to c} f(x)=l\) and \(\displaystyle \lim_{x\to c} f(x)=m\), then \(l\) is always equal to \(m\).

Which of these are true?

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.

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