- #1

Hernaner28

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Hi, I've been trying to proof this with a partner and we couldn't, we tried to apply the definition of limit and continuity but we didn't get anything. This is the problem:

"Let f a function which satisfies $$|f(x)|\leq|x| \forall{x\in{\mathbb{R}}}$$

Proof that is continuous at 0.

Thanks!

PD: I forgot to say that I figured out what f(0) is. And it's obviously 0 because the absolute value cannot be less than 0:

$$|f(0)|<=|0|$$ then $$f(0)=0$$ . But I just don't know how to apply the definition.. do I have to find the epsilon or delta? Thanks for answering!

"Let f a function which satisfies $$|f(x)|\leq|x| \forall{x\in{\mathbb{R}}}$$

Proof that is continuous at 0.

Thanks!

PD: I forgot to say that I figured out what f(0) is. And it's obviously 0 because the absolute value cannot be less than 0:

$$|f(0)|<=|0|$$ then $$f(0)=0$$ . But I just don't know how to apply the definition.. do I have to find the epsilon or delta? Thanks for answering!

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