Compute the indicated limit. (a) limx →3^+ (1)/((x-3)^2) (b) limx →3^- (1)/((x-3)^2)

Name: Problem 14, Chapter 2: Applied Calculus For Business, Economics, and Finance
Uploaded: 2021-03-14T18:04:58-08:00
Duration: 1 min 20 s
Channel: Dwijendra Rao
Description: Compute the indicated limit. (a) limx →3^+ (1)/((x-3)^2) (b) limx →3^- (1)/((x-3)^2)

step 1 Hello we have to find this limit the limit extends to 3 plus 1 upon x minus 3 whole square as we

Compute the indicated limit. (a) limx →3^+ (1)/((x-3)^2) ...

Key Concepts

Limits

A limit describes the value that a function approaches as the input approaches a certain value. It is a fundamental concept in calculus, forming the groundwork for defining derivatives and integrals. Understanding limits involves analysing how a function behaves near points of interest or discontinuities, rather than solely at those points.

One-Sided Limits

One-sided limits consider the behavior of a function as the input approaches a particular value from one specified side—either from the left (denoted by ‘^-’) or from the right (denoted by ‘^+’). This concept is crucial when the function behaves differently on either side of a point, often due to discontinuities or restrictions in the domain.

Infinite Limits

Infinite limits occur when the value of a function increases or decreases without bound as the input approaches a specific point. Such limits indicate that the function approaches infinity or negative infinity, signifying a type of divergence which is crucial in understanding vertical asymptotes and the overall behavior of rational functions near points of discontinuity.

Vertical Asymptotes

Vertical asymptotes are vertical lines where a function's value becomes unbounded as the input nears a certain value. They occur typically when the denominator of a rational function goes to zero while the numerator does not, leading to limits that approach infinity or negative infinity. This concept helps in analyzing and graphing the behavior of functions near points where they are not defined.

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