Question

Lim=(2x^2-x-1)/(x^2-1)x 1через дискриминант

Answer 1

Вот пошаговое решение
Ответ: 1,5

Answer 2

To find the limit of the given expression as x approaches 1, you can use the concept of the limit and evaluate it using the discriminant to handle any potential indeterminate form that may arise.

The given expression is: Lim(x->1) [(2x^2 - x - 1)/(x^2 - 1)] * x

Step 1: Simplify the expression First, simplify the expression inside the limit by factoring the numerator and denominator:

Numerator: 2x^2 - x - 1 = (2x + 1)(x - 1)

Denominator: x^2 - 1 = (x + 1)(x - 1)

Now, the expression becomes: Lim(x->1) [(2x + 1)(x - 1)/((x + 1)(x - 1))] * x

Step 2: Cancel out the common factor of (x - 1) in the numerator and denominator: Lim(x->1) [2x + 1)/(x + 1)] * x

Step 3: Substitute x = 1 into the expression Now, you can directly substitute x = 1 into the simplified expression: Lim(x->1) [(2 * 1 + 1)/(1 + 1)] * 1 = Lim(x->1) (3/2) * 1 = 3/2

Therefore, the limit of the given expression as x approaches 1, using the discriminant to handle the indeterminate form, is 3/2.