How to find the left and right hand limit by not using a calculator

The video tutorial discusses the concept of limits in calculus, focusing on situations where limits do not exist. It begins by explaining the failure of direct substitution and explores alternative methods like factoring and rationalizing. The instructor then demonstrates how to use left and right hand limits to analyze the behavior of a graph near a point where the limit does not exist. The tutorial emphasizes understanding the behavior of functions and the importance of evaluating limits from both sides to determine their existence.

What method can be used to evaluate limits when direct substitution indicates that the limit does not exist?

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Explain how left-hand and right-hand limits can help determine the behavior of a function at a point where the limit does not exist.

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What value was chosen to evaluate the left-hand limit as it approaches 2?

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Describe the outcome of evaluating the left-hand limit based on the calculations provided.

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What conclusion can be drawn about the right-hand limit as it approaches 2 based on the discussion?

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