If limx →c f(x)=64, then limx →c √(f(x))= .

Name: Problem 3, Chapter 1: Calculus, Early Transcendentals
Uploaded: 2021-07-24T22:03:52-08:00
Duration: 3 min 17 s
Channel: N / A
Description: If limx →c f(x)=64, then limx →c √(f(x))= .

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Key Concepts

Limit

The concept of a limit is central in calculus and describes the value that a function approaches as the input approaches some value. In this context, knowing the limit of f(x) as x approaches c helps in determining the behavior of the function near that point.

Continuity

Continuity is the property of a function where small changes in the input result in small changes in the output, and there are no interruptions or jumps in the function's graph. When a function is continuous at a point, the limit as the input approaches that point is equal to the function's value at that point.

Function Composition and Limit Laws

The limit laws state that the limit of a composition of functions is the function of the limit, provided the outer function is continuous at the limit of the inner function. This allows us to 'move' the limit operation inside a continuous function like the cube root.

Cube Root Function

The cube root function is continuous over all real numbers, meaning that the cube root of the limit of a function is equal to the limit of the cube root of the function. This property is used to simplify the calculation of limits involving cube roots.

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