Evaluate lim x→2^+ √x−2.

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Identify the type of limit: This is a one-sided limit as x approaches 2 from the right (x→2^+).

Understand the behavior of the function: As x approaches 2 from the right, x is slightly greater than 2, so x - 2 is a small positive number.

Consider the expression under the square root: Since x is approaching 2 from the right, the expression \( \sqrt{x - 2} \) involves taking the square root of a small positive number.

Analyze the limit: As x gets closer to 2 from the right, the value of \( x - 2 \) approaches 0, making \( \sqrt{x - 2} \) approach the square root of 0.

Conclude the behavior of the limit: The limit of \( \sqrt{x - 2} \) as x approaches 2 from the right is the square root of 0.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Limits

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. In this case, we are interested in the limit as x approaches 2 from the right (denoted as 2^+). Understanding limits is crucial for analyzing the continuity and behavior of functions at specific points.

Square Root Function

The square root function, denoted as √x, is a function that returns the non-negative value whose square is x. In the context of the limit, we are evaluating √x - 2 as x approaches 2. Understanding the properties of the square root function, including its domain and behavior near specific points, is essential for accurately calculating the limit.

Evaluate lim x→2^+ √x−2.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Limits

One-Sided Limits

Square Root Function