Question

Lim x^3+8/ -2x^3+3x+1 x=стремится к беспокнечности

Answer 1

Решение в приложении.

Answer 2

To evaluate the limit of the given function as x approaches infinity, we need to divide both the numerator and denominator by the highest power of x in the denominator, which is x^3. This gives:

lim x^3+8/ -2x^3+3x+1 = lim (x^3/x^3 + 8/x^3) / (-2x^3/x^3 + 3x/x^3 + 1/x^3)

Now, as x approaches infinity, all the terms with powers of x in the denominator tend to zero. Therefore, we can simplify the expression as:

lim x^3+8/ -2x^3+3x+1 = lim (1 + 8/x^3) / (-2 + 3/x^2 + 1/x^3)

As x approaches infinity, the second term in the denominator (3/x^2) and the third term (1/x^3) both tend to zero, so we can ignore them. Thus, we have:

lim x^3+8/ -2x^3+3x+1 = lim (1 + 8/x^3) / (-2)

Evaluating this limit, we get:

lim x^3+8/ -2x^3+3x+1 = (1 + 0) / (-2) = -1/2

Therefore, the limit of the given function as x approaches infinity is -1/2.