Question

Lim x стремиться к -1....... x^3-3x-2/x^2-x-2

Answer 1

Смотри,,,,,,,,,,,,,,,,,,,,

Answer 2

Найти предел.

$\lim\limits_{x\to -1} \dfrac{x^3-3x-2}{x^2-x-2} = \left[\dfrac{0}{0}\right] = \lim\limits_{x\to -1} \dfrac{(x^3-3x-2)'}{(x^2-x-2)'} = \lim\limits_{x\to -1} \dfrac{(3x^2)_{\to 3} - 3}{(2x)_{\to-2} - 1} = \\ =\lim\limits_{x\to -1} \dfrac{3-3}{-2-1} = \dfrac{0}{-3} = 0.$

Используется правило Лопиталя.

Ответ: 0.

Answer 3

To find the limit of the expression (x^3 - 3x - 2) / (x^2 - x - 2) as x approaches -1, we can directly substitute -1 into the expression and evaluate it.

Substituting x = -1, we get:

((-1)^3 - 3(-1) - 2) / ((-1)^2 - (-1) - 2) = (-1 + 3 - 2) / (1 + 1 - 2) = 0 / 0

We obtained an indeterminate form of 0/0, which means we cannot determine the limit of the expression by direct substitution. To proceed, we can factorize the numerator and denominator and simplify the expression.

Factoring the numerator: x^3 - 3x - 2 = (x + 1)(x^2 - x - 2) = (x + 1)(x - 2)(x + 1) = (x - 2)(x + 1)^2

Factoring the denominator: x^2 - x - 2 = (x + 1)(x - 2)

Now we can simplify the expression: [(x - 2)(x + 1)^2] / [(x + 1)(x - 2)]

Notice that (x - 2) and (x + 1) cancel out in the numerator and denominator, leaving us with:

(x + 1)

Since the common factors canceled out, we can now substitute x = -1 into the simplified expression:

(x + 1) = (-1 + 1) = 0

Therefore, the limit of the expression as x approaches -1 is 0.