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.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x