Question

Lim х стремится к 1 х-√х/х²-х

Answer 1

Решение прицеплено на картинке.

Answer 2

To find the limit of the expression (1-√x)/(x²-x) as x approaches 0, we can use algebraic manipulation and L'Hôpital's rule.

First, we can simplify the expression by multiplying the numerator and denominator by the conjugate of the numerator, which is (1+√x). This gives us:

(1-√x)/(x²-x) * (1+√x)/(1+√x) = (1 - x)/(x*(1+√x)*(1-√x))

Next, we can simplify the denominator by noticing that (1-√x) and (1+√x) are conjugates, so their product is simply 1-x. This gives us:

(1 - x)/(x*(1+√x)(1-√x)) = 1/(x(1+√x))

Now we can use L'Hôpital's rule to evaluate the limit. Taking the derivative of the numerator and denominator with respect to x, we get:

lim(x->0) 1/(x*(1+√x)) = lim(x->0) (1+√x)/(x) = ∞

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