Use the properties of limits to help decide whether each limit exists. If limit exits, find its value.
a. lim_x-->[infinity] x^4 - x^3 - 3x / 7x^2 + 9
b. lim_x-->25 √x - 5 / x - 25

a) The limit doesnt exist.

b) The limit exists and its value is 1/10

Step-by-step explanation:

a) We take the highest power (x⁴) as common factor in both the numerator and the denominator.

The limit of the numerator is 1 (when x goes to infinity) and the limit on the second part is 0. Hence the limit doesnt exist (it goes to infinity).

b) Note that if we multiply √x - 5 by its conjugate of , which is √x + 5, we obtain x - 25, thus

Hence, the limit exists and its value is 1/10.

Emilias inequality, x<6 is correct because the number of hours is less than it equal to 6. Emilias number line is correct. The endpoint is correctly filled in and the number line should be shaded to the left of the endpoint.