Question

Find the limit as x approaches negative infinity for the function h(x) = (3x² + 2x - 1)/(x² - 5x + 4).

a) 3
b) -3
c) 2
d) -2

Answer 1

The limit as x approaches negative infinity for the function h(x) is 3, which is found by comparing the coefficients of the highest-degree terms in the numerator and the denominator.

Step-by-step explanation:

To find the limit as x approaches negative infinity for the function h(x) = (3x² + 2x - 1)/(x² - 5x + 4), we observe that both the numerator and the denominator are polynomials of the same degree (degree 2 in this case). We can find the limit by comparing the coefficients of the highest-degree terms in the numerator and the denominator.

As x goes to negative infinity, the terms with lower degrees of x become insignificant in comparison to the terms with x². Hence we can disregard them and only consider the leading coefficients of the x² terms. This gives us the ratio of the leading coefficients: 3/1, which is simply 3.

Thus, the limit as x approaches negative infinity for the function h(x) is 3.