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Problem 78

Determining a Limit In Exercises 77 and $78,$ consider the function $f(x)=\sqrt{x}$ .

Is $$\lim _{x \rightarrow 0} \sqrt{x}=0$$ a true statement? Explain.

Answer

$\lim _{x \rightarrow 0} \sqrt{x}=0$

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## Discussion

## Video Transcript

and this problem, we want to prove or disprove the claim. The limit is X approaches. Zero of the function of X equals a squared of x zero. So let's consider the graph of X equals the square root of X. Here, to the left is a sketch of the novaks. So we see that if we approach X equals zero from the right, the graph is getting closer and closer. Two, sir. Here for the right hand limit. Zero. However, there is no limit from the left hand side. So we wondered, Does this mean that'll limit is undefined? Well, yes and no. Since the square root of X is only defined for X values greater than or equal 20 we know that negative numbers are not the domain off our function. So it's not that the limit doesn't exactly exist there. It's just totally under find there. So since X equals zero is an end point and the limit from the right exists, we know that the limit has affects approaches. Zero is in fact, people to zero