Suppose limx→4 f(x) = 0 and lim x→4 g(x) = −3. Find

c. limx→4 (g(x))²

검증된 단계별 안내

First, understand that the problem involves finding the limit of a function as x approaches a certain value. In this case, we are looking for lim_x→4 (g(x))².

Recall the limit property: if lim_x→a g(x) = L, then lim_x→a (g(x))² = L², provided the limit exists.

Given that lim_x→4 g(x) = -3, we can apply this property to find the limit of (g(x))².

Substitute the known limit value into the expression: lim_x→4 (g(x))² = (-3)².

Finally, calculate the square of the limit value: (-3)². This will give you the limit of (g(x))² as x approaches 4.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Limit of a Function

The limit of a function describes the value that a function approaches as the input approaches a certain point. In this case, we are interested in the behavior of the functions f(x) and g(x) as x approaches 4. Understanding limits is fundamental in calculus, as it lays the groundwork for concepts such as continuity and derivatives.

Properties of Limits

Limits have several properties that simplify the evaluation of expressions. One important property is that the limit of a product or a power can be computed using the limits of the individual functions. Specifically, if limx→a g(x) exists, then limx→a (g(x))² = (limx→a g(x))², which allows us to find the limit of g(x) squared directly from the limit of g(x).

Continuous Functions

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. While the question does not explicitly state continuity, knowing that limits exist for both f(x) and g(x) suggests that g(x) behaves predictably around x = 4, allowing us to confidently compute the limit of (g(x))².

Suppose limx→4 f(x) = 0 and lim x→4 g(x) = −3. Findc. limx→4 (g(x))²