Determine the following limits.

a. lim x→2^+ 1 x − 2

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

Recognize the form of the function: The function is \( \frac{1}{x - 2} \).

Consider the behavior of \( x - 2 \) as \( x \to 2^+ \): As \( x \) approaches 2 from the right, \( x - 2 \) becomes a small positive number.

Analyze the behavior of the function: Since \( x - 2 \) is a small positive number, \( \frac{1}{x - 2} \) becomes a large positive number.

Conclude the limit: The limit of \( \frac{1}{x - 2} \) as \( x \to 2^+ \) is positive infinity.

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주요 개념

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Limits

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It helps in understanding how functions behave near points of interest, including points of discontinuity or infinity. The notation 'lim x→a f(x)' indicates the value that f(x) approaches as x gets arbitrarily close to a.

Infinite Limits

An infinite limit occurs when the value of a function increases or decreases without bound as the input approaches a certain point. In the context of the given limit, 'lim x→2^+ 1/(x - 2)', as x approaches 2 from the right, the denominator approaches zero, causing the function to approach positive infinity. This concept is essential for analyzing vertical asymptotes in rational functions.

Determine the following limits.a. lim x→2^+ 1 x − 2

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Limits

One-Sided Limits

Infinite Limits

Determine the following limits.

a. lim x→2^+ 1 x − 2