Question

Evaluate lim[x → -[infinity]] (sqrt[x² - 3x] / [1 - x]).

a) 1
b) 0
c) -1
d) Does not exist

Answer 1

To evaluate the limit lim[x → -∞] (sqrt(x² - 3x) / (1 - x)), simplify the expression by considering the highest power of x in the numerator and denominator. The limit is -1.

Step-by-step explanation:

To evaluate the limit lim[x → -∞] (sqrt(x² - 3x) / (1 - x)), we need to simplify the expression. Since we are approaching negative infinity, we can consider only the highest power of x in the numerator and denominator.

The highest power of x in the numerator is x and in the denominator is -x. So, the limit becomes lim[x → -∞] (x / -x). Simplifying this further, the limit is equal to lim[x → -∞] -1. Therefore, the answer is c) -1.