Question

Lim (x -> [infinity]) √(144x²x) - 12x
a) 144
b) [infinity]
c) 0
d) 1/12

Answer 1

The limit of the expression as x approaches infinity is √(144x³) = 12x^(3/2).

Step-by-step explanation:

To find the value of the given limit, we can simplify the expression first. The expression can be written as:

√(144x²x) - 12x

Next, we can factor out x from inside the square root:

= √(144x³) - 12x

Using the rule √(a³) = a^(3/2), we can simplify further:

= (12x)^(3/2) - 12x

Now, as x approaches infinity, the second term -12x becomes increasingly insignificant compared to the first term. Therefore, the limit of the expression as x approaches infinity is √(144x³) = 12x^(3/2).

So the answer is (b) infinity.