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University of California, Berkeley

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Problem 83

Proof Prove that

$$\lim _{x \rightarrow c} f(x)=L$$

is equivalent to

$$\lim _{x \rightarrow c}[f(x)-L]=0$$

Answer

$$\lim _{x \rightarrow c}[f(x)-L]=0$$

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## Discussion

## Video Transcript

Okay, so we have the limit as experts see from our function. So it's the truck out from both sides that I put you down and then we need to apply our limits. We have the limit. Is that so? To speak over function minus the limit. Next to see about you could get a limit as a clipper to see, actually that Oh, and there are constant sort of limited them is just a constant. You were left with the limit. Exactly. Take with you. Oh, if we could sell, Which means that limit, as expected, okay of our absolute value might sound is also equal to go.