Question

Lim x -бесконечность 3x^2-7x+4/2x+5x^2

Answer 1

= lim x стремится к бесконечности 7x^3/5x^4 = lim x стремится к бесконечности 7/5x = 7/бесконечность = 0.

Answer 2

To find the limit as x approaches negative infinity of the given expression:

lim (x -> -∞) (3x^2 - 7x + 4) / (2x + 5x^2)

We can use the concept of "dominant terms" in the numerator and denominator, which means we focus on the highest power terms of x.

As x approaches negative infinity, the term with the highest power in the numerator (3x^2) and the denominator (5x^2) will dominate the behavior of the expression.

So, let's ignore all other terms and simplify the expression by considering only the dominant terms:

lim (x -> -∞) (3x^2) / (5x^2)

Now, we can cancel out the common factor of x^2 from the numerator and denominator:

lim (x -> -∞) (3/5)

As x approaches negative infinity, the expression converges to 3/5.

Therefore, the limit of the given expression as x approaches negative infinity is 3/5.