Limited!

Calculus Level 4

Read the statements carefully.

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

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

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

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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