- #1

Eclair_de_XII

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- 91

- Homework Statement
- "Let ##f(x)=\sqrt{x}##. Prove or disprove ##\lim_{x\rightarrow0} \sqrt{x}=0##."

- Relevant Equations
- A function ##f## has a limit ##L## at ##a## iff ##\lim_{x\rightarrow a^-}=L=\lim_{x\rightarrow a^+}##.

Instinct tells me to just plug in the number, say the limit is zero, and be done with it. But at the same time, while reading the statement from the "Relevant equations" section of this post, I cannot feel but feel some doubt as to whether or not this is the right approach. I mean, only the right-sided limit is defined, while the left-sided limit isn't. So am I to conclude that since the root function doesn't even have a left-handed limit, that I don't need to worry about the statement in the "Relevant equations" section?

Sorry; it's been many years since I last took Calculus I, so I am sorry for being dense when it comes to simple concepts like this.

Sorry; it's been many years since I last took Calculus I, so I am sorry for being dense when it comes to simple concepts like this.