Question

Lim x->бесконечность x^3+2x/x^2-4

Answer 1

Пошаговое объяснение:

1) lim x стремиться к бесконечности (2x-5/2x+3)^7x

2) lim x стремиться к +бесконечности (x -корень из x^2 -x+1)

3) lim x стремиться к нулю tgx+sinx/2x

4) lim x стремиться к единице 2x^3 - 2x^2 + x -1/ x^3- x^2 +3x -3

5) lim x стремиться к бесконечности 5x^3 -x^2+4/-7^3+x

Answer 2

To find the limit of the given expression as x approaches infinity, we can simplify the expression and analyze the behavior of the terms.

Let's simplify the expression: (x^3 + 2x) / (x^2 - 4).

Dividing both the numerator and denominator by x^2, we get: (x^3/x^2 + 2x/x^2) / (x^2/x^2 - 4/x^2) Simplifying further: (x + 2/x) / (1 - 4/x^2)

As x approaches infinity, the terms 2/x and 4/x^2 tend to zero since the denominator grows much faster than the numerator. Therefore, we have: (x + 2/x) / (1 - 4/x^2) ≈ (x + 0) / (1 - 0) = x / 1 = x.

Hence, as x approaches infinity, the expression x^3 + 2x / (x^2 - 4) approaches infinity.