Question

Lim x к бесконечности = (4x²-7x³-2x^5)/(4x^5-6x⁴+8x²)

Answer 1

Решение на фотографии

Answer 2

Так как лимит стремится к бесконечности, то мы берем отношения лишь старших членов (это члены, степень которых наивысшая в делимом и делителе; в данном случае 5 - наибольшая степень и в числителе, и в знаменателе):
lim=(-2x^5)/(4x^5)=-1/2

Answer 3

To find the limit of the given expression as x approaches infinity, we need to examine the highest degree terms in the numerator and denominator. Let's simplify the expression by dividing both the numerator and denominator by the highest power of x, which is x^5:

(4x² - 7x³ - 2x^5) / (4x^5 - 6x^4 + 8x²)

Dividing both numerator and denominator by x^5:

(4x²/x^5 - 7x³/x^5 - 2x^5/x^5) / (4x^5/x^5 - 6x^4/x^5 + 8x²/x^5)

Now simplify:

(4/x^3 - 7/x^4 - 2) / (4 - 6/x + 8/x^3)

As x approaches infinity, the terms with x in the denominator will tend to zero, and the expression becomes:

(0 - 0 - 2) / (4 - 0 + 0) = -2/4 = -1/2

So, the limit of the given expression as x approaches infinity is -1/2.