Right/left hand limit as x approaches to 0

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SUMMARY

The discussion focuses on determining the right and left hand limits of the function h(x) as x approaches 0, 1, and 2. It establishes that as x approaches 0 from the left, the limit is equivalent to lim_{x→0^-} f(x) = x, while from the right, it is lim_{x→0^+} f(x) = x². The conversation clarifies the definitions and calculations of one-sided limits in calculus, providing a clear understanding of how to evaluate them for specific functions.

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Homework Statement


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Homework Equations



I trying to figure out if how will you know if which of the following h(x) will be the right/left hand limit as x approaches to 0, as x approaches to 1, as x approaches to 2? I'm confused... please help

The Attempt at a Solution


I really don't have any idea
 
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To the left of 0, f(x) is identical to x. Do you know how to do lim_{x\rightarrow 0} x? If so, that is exactly lim_{x\rightarrow 0^-} f(x).

Just to the right of 0, f(x) is identical to x2 and so the "limit from the right", \lim_{x\rightarrow 0^+} f(x) is the same as \lim_{x\rightarrow 0} x^2.
 

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