# Limited!

Calculus Level 4

$$[1]$$. 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?

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